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A new subspace approach is proposed for enhancement of speech corrupted by colored noise. The proposed approach is based on the simultaneous diagonalization of the clean speech and noise covariance matrices, which leads to an optimal linear estimator that minimizes speech distortion subject to the noise distortion being below a set threshold. The proposed approach is shown to be a generalization of the approach proposed by Ephraim and Van Trees (1995) for white noise. Objective and subjective measures demonstrated significant improvements over other subspace-based methods when tested with sentences corrupted with speech-shaped noise and multitalker babble.