  We investigate the quark masses and mixings by including vector-like down-type quark singlets in universality of strength for Yukawa couplings (USY). In contrast with the standard model with USY, the sufficient $ CP $ violation is obtained for the Cabibbo-Kobayashi-Maskawa matrix through the mixing between the ordinary quarks and quark singlets. The top-bottom mass hierarchy $ m_t \gg m_b $ also appears naturally in the USY scheme with the down-type quark singlets. 
Universality of strength for Yukawa couplings with extra down-type quark   singlets