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Blind source separation for convolutive mixtures can be solved effectively in the frequency domain where independent component analysis is performed in each frequency independently. However, the permutation problem arises: the permutation ambiguity of ICA in each frequency bin should be aligned so that a separated signal in the time-domain contains frequency components of the same source signal. In this paper, we present a new method for solving the permutation problem using microphone sub-arrays. It is based on the combination of two approaches: direction of arrival (DOA) estimation for sources and the inter-frequency correlation of signal envelopes. First, DOA estimation is performed using microphone sub-arrays so that the permutation problem is solved more robustly in low frequencies. Second, we exploit the correlation between the adjacent bins to fix the permutation for the remaining frequencies. Experimental results show that the proposed method provided a more robust solution to the permutation problem in a real acoustic environment.