  The transfer matrix method is usually employed to study problems described by
$N$ equations of matrix Sturm-Liouville (MSL) kind. In some cases a numerical
degradation (the so called $\Omega d$ problem) appears thus impairing the
performance of the method. We present here a procedure that can overcome this
problem in the case of multilayer systems having piecewise constant
coefficients. This is performed by studying the relations between the
associated transfer matrix and other transfer matrix variants. In this way it
was possible to obtain the matrices which can overcome the $\Omega d$ problem
in the general case and then in problems which are particular cases of the
general one. In this framework different strategies are put forward to solve
different boundary condition problems by means of these numerically stable
matrices. Numerical and analytic examples are presented to show that these
stable variants are more adequate than other matrix methods to overcome the
$\Omega d$ problem. Due to the ubiquity of the MSL system, these results can be
applied to the study of many elementary excitations in multilayer structures.
