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In this paper, a novel information the-ory criterion is proposed for blind source separationbased on a fully recurrent neural network, and a lea-ing algorithm is then developed. Stochastic naturalgradient descent algorithm is used in this algorithm.The proposed algorithm can ensure the maximizationof transferred information when a Hebb term is intro-duced to express the derivative of information missing.At the same time, the mutual information of outputs isminimized so as to make the outputs mutually statis-tically independent. The computer simulation showsthe validity and the good performance of the proposedalgorithm.