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Binaural hearing aids include a wireless link to exchange the signals received at each side, allowing the implementation of more efficient noise-reduction algorithms for hostile environments such as babble noise. Although several binaural noise-reduction techniques have been proposed in the literature, only a few of them preserve localization cues of the target and interfering signals simultaneously without degrading the SNR improvement. This paper proposes a novel binaural noise-reduction method based on blind source separation (BSS) and a perceptual post-processing technique. Objective and subjective tests under four different scenarios were performed. The method showed good output sound quality, high SNR improvement at very low input SNR conditions, and preservation of localization cues for the signal and noise - outperforming both an existing BSS-based method and a multichannel Wiener filter (MWF).