  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.
