  We present a numerically stable re-formulization of the transfer matrix
method (TMM). The iteration form of the traditional TMM is transformed into
solving a set of linear equations. Our method gains the new ability of
calculating accurate wave-functions of higher dimensional disordered systems.
It also shows higher efficiency than the traditional TMM when treating finite
systems. In contrast to the diagonalization method, our method not only
provides a new route for calculating the wave-function corresponding to the
boundary conditions of open systems in realistic transport experiments, but
also has advantages that the calculating wave energy/frequency can be tuned
continuously and the efficiency is much higher. Our new method is further used
to identify the necklace state in the two dimensional disordered Anderson
model, where it shows advantage in cooperating the wave-functions with the
continuous transmission spectrum of open systems. The new formulization is very
simple to implement and can be readily generalized to various systems such as
spin-orbit coupling systems or optical systems.
