opinion: Mr. Justice White
  delivered the opinion of the Court.
  This litigation has a protracted history in the courts below and has already resulted in one judgment and opinion by this Court. Dayton Board of Education v. Brinkman, 433 U. S. 406 (1977) (Dayton I). In its most recent opinion, the United States Court of Appeals for the Sixth Circuit approved a systemwide plan for desegregating the public schools of Dayton, Ohio. Brinkman v. Gilligan, 583 F. 2d 243 (1978). The Court of Appeals found that the Dayton Board of Education had operated a racially segregated, dual school system at the time of Brown v. Board of Education, 347 U. S. 483 (1954) (Brown I), and that “'[t]he evidence of record demonstrates convincingly that defendants have failed to eliminate the continuing systemwide effects of their prior discrimination” and “actually have exacerbated the racial separation existing at the time of Brown I.” 583 F. 2d, at 253. We granted certiorari, 439 U. S. 1066 (1979), and heard argument in this case in tandem with Columbus Board of Education v. Penick, ante, p. 449. We now affirm the judgment of the Court of Appeals.
  I
  The public schools of Dayton are highly segregated by race. In the year the complaint was filed, 43% of the students in the Dayton system were black, but 51 of the 69 schools in the system were virtually all white or all black. Brinkman v. Gilligan, 446 F. Supp. 1232, 1237 (SD Ohio 1977). A number of students in the Dayton system, through their parents, brought this action on April 17, 1972, alleging that the Dayton Board of Education, the State Board of Education, and the appropriate local and state officials were operating a racially segregated school system in violation of the Equal Protection Clause of the Fourteenth Amendment. The plaintiffs sought a court order compelling desegregation. The District Court sustained their challenge, determining that certain actions by the Dayton Board amounted to a “cumulative” violation of the Fourteenth Amendment. Id., at 1259. The District Court also approved a plan having limited remedial objectives.
  The District Court’s judgment that the Board had violated the Fourteenth Amendment was affirmed by the Court of Appeals; but after twice being reversed on the ground that the prescribed remedy was inadequate to eliminate all vestiges of state-imposed segregation, the District Court ordered the Board to take the necessary steps to assure that each school in the system would roughly reflect the systemwide ratio of black and white students. App. to Pet. for Cert. 103a. The Court of Appeals then affirmed. Brinkman v. Gilligan, 539 F. 2d 1084 (1976).
  We reversed the judgment of the Court of Appeals and ordered the case remanded to the District Court for further proceedings. Dayton I, supra. In light of the District Court’s limited findings regarding liability, we concluded that there was no warrant for imposing a systemwide remedy. Rather, the District Court should have “determine [d] how much incremental segregative effect these violations had on the racial distribution of the Dayton school population as presently constituted, when that distribution is compared to what it would have been in the absence of such constitutional violations. The remedy must be designed to redress that difference, and only if there has been a systemwide impact may there be a systemwide remedy.” 433 U. S., at 420. In view of the confusion evidenced at various stages of the proceedings regarding the scope of the violation established, we remanded the case to permit supplementation of the record and specific findings addressed to the scope of the remedy, id., at 418-419, but allowed the existing remedy to remain in effect on remand subject to further orders of the District Court, id., at 420-421.
  The District Court held a supplemental evidentiary hearing, undertook to review the entire record anew, and entered findings of fact and conclusions of law and a judgment dismissing the complaint. In support of its judgment, the District Court observed that, although various instances of purposeful segregation in the past evidenced “an inexcusable history of mistreatment of black students,” 446 F. Supp., at 1237, plaintiffs had failed to prove that acts of intentional segregation over 20 years old had any current incremental segregative effects. The District Court conceded that the Dayton schools were highly segregated but ruled that the Board's failure to alleviate this condition was not actionable absent sufficient evidence that the racial separation had been caused by the Board's own purposeful discriminatory conduct. In the District Court's eyes, plaintiffs had failed to show either discriminatory purpose or segregative effect, or both, with respect to the challenged practices and policies of the Board, which included faculty hiring and assignments, the use of optional attendance zones and transfer policies, the location and construction of new and expanded school facilities, and the rescission of certain prior resolutions recognizing the Board’s responsibility to eradicate racial separation in the public schools.
  The Court of Appeals reversed. The basic ingredients of the Court of Appeals’ judgment were that at the time of Brown I, the Dayton Board was operating a dual school system, that it was constitutionally required to disestablish that system and its effects, that it had failed to discharge this duty, and that the consequences of the dual system, together with the intentionally segregative impact of various practices since 1954, were of systemwide import and an appropriate basis for a systemwide remedy. In arriving at these conclusions, the Court of Appeals found that in some instances the findings of the District Court were clearly erroneous and that in other respects the District Court had made errors of law. 583 F. 2d, at 247. Petitioners contend that the District Court, not the Court of Appeals, correctly understood both the facts and the law.
  II
  A
  The Court of Appeals expressly held that, “at the time of Brown I, defendants were intentionally operating a dual school system in violation of the Equal Protection Clause of the fourteenth amendment,” and that the “finding of the district court to the contrary is clearly erroneous.” 583 F. 2d, at 247 (footnote omitted). On the record before us, we perceive no basis for petitioners’ challenge to this holding of the Court of Appeals.
  Concededly, in the eariy 1950’s, "77.6 percent of all students attended schools in which one race accounted for 90 percent or more of the students and 54.3 percent of the black students were assigned to four schools that were 100 percent black.” Id., at 248-249. One of these schools was Dunbar High School, which, the District Court found, had been established as a districtwide black high school with an all-black faculty and a black principal, and remained so at the time of Brown I and up until 1962. 446 F. Supp., at 1245. The District Court also found that “among” the early and relatively undisputed acts of purposeful segregation was the establishment of Garfield as a black elementary school. Id., at 1236-1237. The Court of Appeals found that two other elementary schools were, through a similar process of optional attendance zones and the creation and maintenance of all-black faculties, intentionally designated and operated as all-black schools in the 1930’s, in the 1940’s, and at the time of Brown I. 583 F. 2d, at 249, 250-251. Additionally, the District Court had specifically found that in 1950 the faculty at 100% black schools was 100% black and that the faculty at all other schools was 100% white. 446 F. Supp., at 1238.
  These facts, the Court of Appeals held, made clear that the Board was purposefully operating segregated schools in a substantial part of the district, which warranted an inference and a finding that segregation in other parts of the system was also purposeful absent evidence sufficient to support a finding that the segregative actions “were not taken in effectuation of a policy to create or maintain segregation” or were not among the “factors . . . causing the existing condition of segregation in these schools.” Keyes v. School Dist. No. 1, Denver, Colo., 413 U. S. 189, 214 (1973); see id., at 203; Columbus Board of Education v. Penick, ante, at 467-468. The District Court had therefore ignored the legal significance of the intentional maintenance of a substantial number of black schools in the system at the time of Brown 1. It had also ignored, contrary to Swann v. Charlotte-Mecklenburg Board of Education, 402 U. S. 1, 18 (1971), the significance of purposeful segregation in faculty assignments in establishing the existence of a dual school system; here the “purposeful segregation of faculty by race was inextricably tied to racially motivated student assignment practices.” 583 F. 2d, at 248. Based on its review of the entire record, the Court of Appeals concluded that the Board had not responded with sufficient evidence to counter the inference that a dual system was in existence in Dayton in 1954. Thus, it concluded that the Board’s “intentional seg-regative practices cannot be confined in one distinct area”; they “infected the entire Dayton public school system.” Id., at 252.
  B
  Petitioners next contend that, even if a dual system did exist a quarter of a century ago, the Court of Appeals erred in finding any widespread violations of constitutional duty since that time.
  Given intentionally segregated schools in 1954, however, the Court of Appeals was quite right in holding that the Board was thereafter under a continuing duty to eradicate the effects of that system, Columbus, ante, at 458, and that the systemwide nature of the violation furnished prima facie proof that current ségregation in the Dayton schools was caused at least in part by prior intentionally segregative official acts. Thus, judgment for the plaintiffs was authorized and required absent sufficient countervailing evidence by the defendant school officials. Keyes, supra, at 211; Swann, supra, at 26. At the time of trial, Dunbar High School and the three black elementary schools, or the schools that succeeded them, remained black schools; and most of the schools in Dayton were virtually one-race schools, as were 80% of the classrooms. “ ‘Every school which was 90 percent or more black in 1951-52 or 1963-64 or 1971-72 and which is still in use today remains 90 percent or more black. Of the 25 white schools in 1972-73, all opened 90 percent or more white and, if open, were 90 percent or more white in 1971-72, 1963-64 and 1951-52.’ ” 583 F. 2d, at 254 (emphasis in original), quoting Brinkman v. Gilligan, 503 F. 2d 684, 694-695 (CA6 1974). Against this background, the Court of Appeals held that “[t]he evidence of record demonstrates convincingly that defendants have failed to eliminate the continuing systemwide effects of their prior discrimination and have intentionally maintained a segregated school system down to the time the complaint was filed in the present case.” 583 F. 2d, at 253. At the very least, defendants had failed to come forward with evidence to deny “that the current racial composition of the school population reflects the systemwide impact” of the Board’s prior discriminatory conduct. Id., at 258.
  Part of the affirmative duty imposed by our cases, as we decided in Wright v. Council of City of Emporia, 407 U. S. 451 (1972), is the obligation not to take any action that would impede the process of disestablishing the dual system and its effects. See also United States v. Scotland Neck Board of Education, 407 U. S. 484 (1972). The Dayton Board, however, had engaged in many post-Brown I actions that had the effect of increasing or perpetuating segregation. The District Court ignored this compounding of the original constitutional breach on the ground that there was no direct evidence of continued discriminatory purpose. But the measure of the post-Brown I conduct of a school board under an unsatisfied duty to liquidate a dual system is the effectiveness, not the purpose, of the actions in decreasing or increasing the segregation caused by the dual system. Wright, supra, at 460, 462; Davis v. School Comm’rs of Mobile County, 402 U. S. 33, 37 (1971); see Washington v. Davis, 426 U. S. 229, 243 (1976). As was clearly established in Keyes and Swann, the Board had to do more than abandon its prior discriminatory purpose. 413 U. S., at 200-201, n. 11; 402 U. S., at 28. The Board has had an affirmative responsibility to see that pupil assignment policies and school construction and abandonment practices “are not used and do not serve to perpetuate or re-establish the dual school system,” Columbus, ante, at 460, and the Board has a “ 'heavy burden’ ” of showing that actions that increased or continued the effects of the dual system serve important and legitimate ends. Wright, supra, at 467, quoting Green v. County School Board, 391 U. S. 430, 439 (1968).
  The Board has never seriously contended that it fulfilled its affirmative duty or the heavy burden of explaining its failure to do so. Though the Board was often put on notice of the effects of its acts or omissions, the District Court found that “with one [counterproductive] exception ... no attempt was made to alter the racial characteristics of any of the schools.” 446 F. Supp., at 1237. The Court of Appeals held that far from performing its constitutional duty, the Board had engaged in “post-1954 actions which actually have exacerbated the racial separation existing at the time of Brown 583 F. 2d, at 253. The court reversed as clearly erroneous the District Court’s finding that intentional faculty segregation had ended in 1951; the Court of Appeals found that it had effectively continued into the 1970’s. This was a systemwide practice and strong evidence that the Board was continuing its efforts to segregate students. Dunbar High School remained as a black high school until 1962, when a new Dunbar High School opened with a virtually all black faculty and student body. The old Dunbar was converted into an elementary school to which children from two black grade schools were assigned. Furthermore, the Court of Appeals held that since 1954 the Board had used some “optional attendance zones for racially discriminatory purposes in clear violation of the Equal Protection Clause.” Id., at 255. The District Court's finding to the contrary was clearly erroneous. At the very least, the use of such zones amounted to a perpetuation óf the existing dual school system. Likewise, the Board failed in its duty and perpetuated racial separation in the schools by its pattern of school construction and site selection, recited by the District Court, see n. 7, supra, that resulted in 22 of the 24 new schools built between 1950 and the filing of the complaint opening 90% black or white. The same pattern appeared with respect to additions of classroom space made to existing schools. Seventy-eight of a total of 86 additions were made to schools that were 90% of one race. We see no reason to disturb these factual determinations, which conclusively show the breach of duty found by the Court of Appeals.
  C
  Finally, petitioners contend that the District Court correctly interpreted our earlier decision in this litigation as requiring respondents to prove with respect to each individual act of discrimination precisely what effect it has had on current patterns of segregation. This argument results from a misunderstanding of Dayton I, where the violation that had then been established included at most a few high schools. See Columbus, ante, at 458 n. 7 and 465-466; nn. 3 and 5, supra. We have found no reason to fault the Court of Appeals’ findings after our remand that a sufficient case of current, systemwide effect had been established. In reliance on its decision in Columbus, the Court of Appeals held:
  “First, the dual school system extant at the time of Brown 1 embraced ‘a systemwide program of segregation affecting a substantial portion of the schools, teachers, and facilities’ of the Dayton schools, and, thus, clearly had systemwide impact. . . . Secondly, the post-1954 failure of defendants to desegregate the school system in contravention of their affirmative constitutional duty obviously had systemwide impact. . . . The impact of defendants’ practices with respect to the assignment of faculty and students, use of optional attendance zones, school construction and site selection, and grade structure and reorganization clearly was systemwide in that the actions perpetuated and increased public school segregation in Dayton.” 583 F. 2d, at 258 (footnote omitted), quoting Keyes, 413 U. S., at 201.
  As we note in Columbus today, this is not a misuse of Keyes, “where we held that purposeful discrimination in a substantial part of a school system furnishes a sufficient basis for an inferential finding of a systemwide discriminatory intent unless otherwise rebutted, and that given the purpose to operate a dual school system one could infer a connection between such a purpose and racial separation in other parts of the school system.” Columbus, ante, at 467-468. See also Swann, 402 U. S., at 26. The Court of Appeals was also quite justified in utilizing the Board’s total failure to fulfill its affirmative duty — and indeed its conduct resulting in increased segregation — to trace the current, systemwide segregation back to the purposefully dual system of the 1950’s and to the subsequent acts of intentional discrimination. See supra, at 537; Columbus, ante, at 464-465; Keyes, supra, at 211; Swann, supra, at 21, 26-27.
  Because the Court of Appeals committed no prejudicial errors of fact or law, the judgment appealed from must be affirmed.
  So ordered.
  [For dissenting opinion of Me. Justice Stewaet, see ante, p. 469.]
  [For dissenting opinion of Me. Justice Powell, see ante, p. 479.]
  The Court of Appeals set out the undisputed statistics:
  “ ‘Enrollment data from the Dayton system reveals the substantial lack of progress that has been made over the past 23 years in integrating the Dayton school system. In 1951-52, of 47 schools, 38 had student enrollments 90 per cent or more one race (4 black, 34 white). Of the 35,000 pupils in the district, 19 per cent were black. Yet over half of all black pupils were enrolled in the four all black schools; and 77.6 per cent of all pupils were assigned to virtual one race schools. “Virtual one race schools” refers to schools with student enrollments of 90 per cent or more one race. In 1963-64, of 64 schools, 57 had student enrollments 90 per cent or more one race (13 black, 44 white). Of the 57,400 pupils in the district, 27.8 per cent were black. Yet 79.2 per cent of all black pupils were enrolled in the 13 black schools; and 88.8 per cent of all pupils were enrolled in such one race schools.
  “Tn 1971-72 (the year the complaint was filed), of 69 schools, 49 had student enrollments 90 per cent or more one race (21 black, 28 white). Of the 54,000 pupils 42.7 per cent were black; and 75.9 per cent of all black students were assigned to the 21 black schools. In 1972-73 (the year the hearing was held) of 68 schools, 47 were virtually one race (22 black, 25 white); fully 80 per cent of all classrooms were virtually one race. (Of the 50,000 pupils in the district, 44.6 per cent were black).
  “‘Every school which was 90 per cent or more black in 1951-52 or 1963-64 or 1971-72 and which is still in use today remains 90 per cent or more black. Of the 25 white schools in 1972-73, all opened 90 per cent or more white and, if open, were 90 per cent or more white in 1971-72, 1963-64 and 1951-52.’ ” Brinkman v. Gilligan, 583 F. 2d 243, 254 (CA6 1978) (emphasis in original), quoting Brinkman v. Gilligan, 503 F. 2d 684, 69<R695 (CA6 1974).
  In the last stages of this litigation, respondents did not press their claims against the state officials. Only the Dayton Board and local officials petitioned for writ of certiorari.
  The violation found by the District Court had three major components: first, the marked racial separation of students, which the Board had made no significant effort to alter; second, the utilization of optional attendance zones, in some cases racially motivated and having significant segregative effect in two high school zones; and third, the Board’s rescission of previously adopted resolutions recognizing the Board’s role in racial segregation and its responsibility to eradicate the existing pattern.
  To preserve continuity, the court exempted enrolled high school students for two academic years. And the court noted that it would evaluate on a case-by-case basis any deviations from the target percentage. The court, moreover, set down certain guidelines to be followed in achieving the redistribution: (1) students would be permitted to attend neighborhood walk-in schools in those neighborhoods where the schools were already within the approved ratios; (2) students would be transported to the nearest available school; and (3) no student would be transported further than two miles or, if traveling that distance would take more time, for longer than 20 minutes. The District Court appointed a master to supervise the logistics of the plan. Certain other particulars were worked out when the master’s report was filed. The plan has now been in effect for three school years.
  The three parts of the violation found by the District Court are discussed in n. 3, supra. Racial imbalance, we noted in Dayton I, is not per se a constitutional violation, and rescission of prior resolutions proposing desegregation is unconstitutional only if the resolutions were required in the first place by the Fourteenth Amendment. 433 U. S., at 413-414. Thus, the scope of liability extended no further than the use of some optional zones, which apparently had a present effect only as to certain high schools, and the rescission of the resolutions so far as they pertained to these high schools. See id., at 412.
  The District Court observed that “[m]any of those practices, if they existed today, would violate the Equal Protection Clause.” 446 F. Supp., at 1236. The court identified certain Board policies as being “among” such practices: until at least 1934, black elementary students were kept separate from white students; until approximately 1950, high school athletics were deliberately segregated by race; and until about the same time, black students at one high school were ordered or induced to sit at the rear of classrooms and suffered other indignities.
  Reviewing the faculty assignment and hiring practices, the District Court found that until at least 1951 the Board’s policies had been intentionally segregative. But in that year the Board instituted a policy of “dynamic gradualism” and “by 1969 all traces of segregation were virtually eliminated.” Id., at 1238-1239. Reasoning that the predominant factor in the racial identifiability of schools is the pupil population and not the faculty, the court ruled that plaintiffs had not established that past discrimination in faculty assignments had an incremental segregative effect.
  Similarly, the court ruled that the plaintiff children had not shown that the Board’s use of attendance zones and transfers denied equal protection. In certain instances, segregative intent had not been satisfactorily demonstrated. In fact, the District Court reversed itself with respect to the high school optional zones it had earlier held unconstitutional. In other instances, current segregative effect had not been proved. Though another high school, Dunbar, had been created and maintained until 1962 as a citywide black high school, the District Court found that because of the increasing black population in that area Dunbar would have been virtually all black by 1960 anyway. And though until the early 1950’s black orphans had been bused past nearby white schools to all-black schools, this “arguably” discriminatory conduct had not been shown by “objective proof” to have any continued segregative effect. Id., at 1241.
  The court also looked to school construction and siting practices. Although 22 of 24 new schools, 78 of 95 additions, and all 26 portable schools built or utilized by the Board between 1950 and 1972 opened virtually all black or all white, and though many of the accompanying decisions appeared to be so without any rationale as to be “haphazard,” the District Court found that the plaintiffs had not shown purposeful segregation. The court also refused to investigate whether the Board had any legitimate grounds for the failure to close some schools and consolidate others when enrollment declined in recent years. Though such a course would have decreased racial separation and saved money, the court found no evidence of discriminatory purpose in those facts. Nor did the court see any hint of impermissible purpose in the Board’s decisions in the 1940’s to supply school services for legally segregated housing projects and to rent elementary school space in such projects.
  Finally, the court held that the Board’s rescission of its earlier resolutions was not violative of the Fourteenth Amendment since, in light of the court’s finding that the current segregation had no unconstitutional origin, the Board had no constitutional obligation to adopt the resolutions in the first place.
  We have no quarrel with our Brother Stewart’s general conclusion that there is great value in appellate courts showing deference to the fact-finding of local trial judges. Ante, at 470-471. The clearly-erroneous standard serves that purpose well. But under that standard, the role and duty of the Court of Appeals are clear: it must determine whether the trial court’s findings are clearly erroneous, sustain them if they are not, but set them aside if they are. The Court of Appeals performed its unavoidable duty in this case and concluded that the District Court had erred. Differing with our dissenting Brothers, we see no reason on the record before us to upset the judgment of the Court of Appeals in this respect.
  We do not deprecate the relevance of segregated faculty assignments as one of the factors in proving the existence of a school system that is dual for teachers and students: but to the extent that the Court of Anneals understood Swann v. Charlotte-Mecklenburg Board of Education as holding that faculty segregation makes out a prima facie case not only of intentionally discriminatory faculty assignments contrary to the Fourteenth Amendment but also of purposeful racial assignment of students, this is an overreading of Swann.
  The Court of Appeals also held that the District Court had not given proper weight to Oliver v. Michigan State Board of Education, 508 F. 2d 178, 182 (CA6 1974), cert. denied, 421 U. S. 963 (1975), where the Court of Appeals had held that “[a] presumption of segregative purpose arises when plaintiffs establish that the natural, probable, and foreseeable result of public officials’ action or inaction was an increase or perpetuation of public school segregation,” and that “[t]he presumption becomes proof unless defendants affirmatively establish that their action or inaction was a consistent and resolute application of racially neutral policies.” We have never held that as a general proposition the foreseeability of segregative consequences makes out a prima facie case of purposeful racial discrimination and shifts the burden of producing evidence to the defendants if they are to escape judgment; and even more clearly there is no warrant in our cases for holding that such foreseeability routinely shifts the burden of persuasion to the defendants. Of course, as we hold in Columbus today, ante, at 464-465, proof of foreseeable consequences is one type of quite relevant evidence of racially discriminatory purpose, and it may itself show a failure to fulfill the duty to eradicate the consequences of prior purposefully discriminatory conduct. See supra, at 535.
  The Board heard from the local National Association for the Advancement of Colored People and other community groups, the Department of Health, Education, and Welfare, the Ohio State Department of Education, and a citizens advisory group the Board had appointed; at times the Board itself expressed its recognition of the problem and of its responsibility, though ultimately it did nothing. 446 F. Supp., at 1251-1252.
  Under the policy of “dynamic gradualism” instituted in 1951, see n. 7, supra, black teachers were assigned to white or mixed schools when the surrounding communities were ready to accept black teachers, and white teachers who agreed were assigned to black schools. App. 182-Ex. By 1969, each school in the system had at least one black teacher. The District Court apparently did not think the post-1951 policy was purposeful discrimination. 446 F. Supp., at 1238-1239. We think the Court of Appeals was completely justified in finding that conclusion to be clearly erroneous on the undisputed facts. As late as the 1968-1969 school year, the Board assigned 72% of all black teachers to schools that were 90% or more black, and only 9% of white teachers to such schools. And faculty segregation disappeared completely only after efforts of the Department of Health, Education, and Welfare under Title VI of the Civil Rights Act of 1964. See 446 F. Supp., at 1238.
  The Court of Appeals found that the District Court had committed clear error in reversing its earlier findings of purpose as to certain optional zones, which the Court of Appeals had earlier affirmed and this Court had not set aside. 583 F. 2d, at 255.
  Petitioners also contend that the respondent children have failed to establish their standing to bring this action. This challenge is dependent on petitioners1 major contentions, for if the Court of Appeals was correct that the current, systemwide segregation is a result of past unlawful conduct then respondents, as students in the system, clearly have standing.