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A nonlocally weighted soft-constrained natural gradient iterative method is introduced for robust blind separation in reverberant environment. The scaling degree of freedom is controlled by soft-constraints built into the auxillary difference equations. The small divisor problem of iterations in silence durations of speech is resolved. Computations on synthetic speech mixtures based on measured binaural room impulse responses show that the algorithm achieves consistently higher signal-to-interference ratio improvement (SIRI) than existing methods in enclosed rooms with reverberation time up to 1 second. At 1 second reverberation time, 5 decibel (dB) SIRI is achieved; while with the help of a spectral subtraction dereverberation technique for preprocessing, 9 dB of SIRI is obtained.