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Blind source extraction (BSE) is often posed as the maximization of a statistical criterion under a unitary constraint. This paper addresses the convergence problem of a kurtosis-based criterion in the presence of noise. We present the stationary points of such criterion, and show that these extrema are simplified as the minimum mean square error (MMSE) solutions with some approximations. Moreover, we introduce a robust preprocessing approach, which allows one to find the MMSE separation matrix up to an orthogonal factor. The excellent performance of the BSE algorithm based on this preprocessing approach shows that the analysis of the stationary point is reliable.