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Different noise-reduction methods have been proposed in the literature for single and multiple-microphone applications. For binaural hearing aids, multiple-microphone noise-reduction methods offer two significant psycho-acoustical advantages with respect to the single-microphone methods. First, noise reduction strategies based on binaural processing (processing using the information received at the left and right ear) are more effective than using independent monaural processing because of the added information. Second, there is an user preference for noise reduction methods that preserve localization cues of both target and interfering signals. Although different multiple-microphone noise-reduction techniques have been proposed in the literature, only a small set is able to preserve the localization cues for both target and interfering signals. This paper proposes a binaural noise-reduction method that preserves the localization cues for both target and interfering signals. The proposed method is based on blind source separation (BSS) followed by a postprocessing technique inspired by a human auditory model. The performance of the proposed method is analyzed using objective and subjective measurements, and compared to existing binaural noise-reduction methods based on BSS and multichannel Wiener filter (MWF). Results show that for some scenarios and conditions, the proposed method outperforms on average the existing methods in terms of noise reduction and provides nearly similar sound quality.