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Cochannel (two-talker) speech separation is predominantly addressed using pretrained speaker dependent models. In this paper, we propose an unsupervised approach to separating cochannel speech. Our approach follows the two main stages of computational auditory scene analysis: segmentation and grouping. For voiced speech segregation, the proposed system utilizes a tandem algorithm for simultaneous grouping and then unsupervised clustering for sequential grouping. The clustering is performed by a search to maximize the ratio of between- and within-group speaker distances while penalizing within-group concurrent pitches. To segregate unvoiced speech, we first produce unvoiced speech segments based on onset/offset analysis. The segments are grouped using the complementary binary masks of segregated voiced speech. Despite its simplicity, our approach produces significant SNR improvements across a range of input SNR. The proposed system yields competitive performance in comparison to other speaker-independent and model-based methods.