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This paper describes a new method for solving the permutation problem in frequency-domain blind source separation (FDBSS). The permutation problem in FDBSS is the well-known order-changing problem of separating spectra, which is caused by the independent separating process in each frequency bin. The new solution is based on the expectation-maximization (EM) technique applied to phases of inverse separating filters. The EM algorithm treats spatial aliasing implicitly and exploits statistics of a room environment embedded in the inverse of separating filters. As a result, it provides more robust performance than other existing methods based on source directions. In addition, it does not require any knowledge of the microphone geometry. Experimental results in reverberant environments demonstrate good performance of the proposed method.