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The blind source separation (BSS) based on K-SCA is discussed in this paper. The first challenging task of this approach is how to estimate the unknown mixing matrix precisely, to solve this problem, the algorithm based on hyperplane membership function is proposed. In contrast to the classical methods, the required key condition on sparsity of the sources can be considerably relaxed, and the algorithm has a good ability of anti-noise. Several experiments involving speech signals show the effectiveness and efficiency of this method.