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In this paper, we propose a novel algorithm for the separation of convolutive speech mixtures using two-microphone recordings, based on the combination of independent component analysis (ICA) and ideal binary mask (IBM), together with a post-filtering process in the cepstral domain. Essentially, the proposed algorithm consists of three steps. First, a constrained convolutive ICA algorithm is applied to separate the source signals from two-microphone recordings. In the second step, we estimate the IBM by comparing the energy of corresponding time-frequency (T-F) units from the separated sources obtained with the convolutive ICA algorithm. The last step is to reduce musical noise caused typically by T-F masking using cepstral smoothing. The performance of the proposed approach is evaluated based on both reverberant mixtures generated using a simulated room model and real recordings. The proposed algorithm offers considerably higher efficiency, together with improved speech quality while producing similar separation performance as compared with a recent approach.