  Accepting validity of self-consistent theory of localization by Vollhardt and
Woelfle, we derive the finite-size scaling procedure used for studies of the
critical behavior in d-dimensional case and based on the use of auxiliary
quasi-1D systems. The obtained scaling functions for d=2 and d=3 are in good
agreement with numerical results: it signifies the absence of essential
contradictions with the Vollhardt and Woelfle theory on the level of raw data.
The results \nu=1.3-1.6, usually obtained at d=3 for the critical exponent of
the correlation length, are explained by the fact that dependence L+L_0 with
L_0>0 (L is the transversal size of the system) is interpreted as L^{1/\nu}
with \nu>1. For dimensions d\ge 4, the modified scaling relations are derived;
it demonstrates incorrectness of the conventional treatment of data for d=4 and
d=5, but establishes the constructive procedure for such a treatment.
Consequences for other variants of finite-size scaling are discussed.
