Abstract:  In order to investigate the reason for different separation matrixes of different algorithms in the linear non-singular mixture of blind signals‚a theoretical result is proved for the modified model of blind signal separation（BSS）： if we only take into account the rotating factors while ignoring the linear proportion zoom factors‚then the ex-act number of the separation matrixes is the factorial of the source number．A new algorithm to get the separation ma-trixes is then proposed．In this algorithm‚the separation matrixes are obtained by solving some quadratic nonlinear e-quations‚and the algebraic theory and second-order statistic method are adopted．Meanwhile‚a method to get the sepa-ration matrixes by means of the matrix transform is also introduced in the paper．The simulation results have verified the correctness of the theoretical result．

Key words:  blind signal separation, separation matrix, simultaneous diagonalization, rotating factor