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In this paper, we propose a new frequency domain approach to blind source separation (BSS) of audio signals mixed in a reverberant environment. We propose a joint diagonalization procedure on the cross power spectral density matrices of the signals at the output of the mixing system 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. The inverse of the mixing system is then used to separate the sources. An efficient dyadic algorithm to resolve the frequency dependent permutation ambiguities that exploits the inherent nonstationarity of the sources is presented. The effect of the unknown scaling ambiguities is partially resolved using an initialization procedure for the ALS algorithm. The performance of the proposed algorithm is demonstrated by experiments conducted in real reverberant rooms. Performance comparisons are made with previous methods.