Abstract: In this paper the generalized selector matrix has been defind. Using this new conception the general form of input-output relationship.,which is eguivalent to the canonical state eguation, has been obtained,and a study is made on the internal relations between the different identification algorithms and between the different canonical forms. On the basis of this study a new simple algorithm of the realization of B^* is proposed. Matrix inversion is not required for whole idea tification process.