  A new effective method for factorization of a class of nonrational $n\times n$ matrix-functions with \emph{stable partial indices} is proposed. The method is a generalization of the one recently proposed by the authors which was valid for the canonical factorization only. The class of considered matrices is motivated by problems originated from applications. The properties and details of the asymptotic procedure are illustrated by examples. The efficiency of the procedure is highlighted by numerical results. 
Factorization of a class of matrix-functions with stable partial indices