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A new improved, easily implementible learning algorithm for blind separation of statistically independent unknown source signals is proposed. In contrast to the well known algorithms, two time trajectories of synaptic weights (wij(t) and (wij(t)) are computed where wij(t) is the time average of wij(t). Extensive computer simulation experiments have confirmed that the proposed learning algorithm assures a high convergence speed of the neural network for a blind identification problem, i.e. a quick recovering of unknown signals from the observation of a linear combination (mixture) of them. The algorithm can easily be extended to other applications.