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We propose a new frequency domain approach to blind source separation (BSS) of audio signals mixed in a reverberant environment. It is first shown that joint diagonalization of the cross power spectral density matrices of the signals at the output of the mixing system is sufficient to identify the mixing system at each frequency bin up to a scale and permutation ambiguity. The frequency domain joint diagonalization is performed using a new and quickly converging algorithm which uses an alternating least-squares (ALS) optimization method. An efficient dyadic algorithm to resolve the frequency dependent permutation ambiguities is presented. The effect of the unknown scaling ambiguities is partially resolved using a novel initialization procedure for the ALS algorithm. The performance of the proposed algorithm is demonstrated by experiments conducted in real reverberant rooms.