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This paper proposes an algorithm for the blind dereverberation of speech signals based on a two-channel linear prediction. Traditional dereverberation methods usually achieve good performance when the input signal is white noise. However, when dealing with colored signals generated by an autoregressive (AR) process such as speech, the generating AR process is deconvolved causing excessive whitening of the signal. This paper proposes a blind dereverberation algorithm that recovers speech signals suffering from deterioration due to the reverberation in a room. We overcome the whitening problem faced by traditional methods by estimating the generating AR process and applying this estimated AR process to the whitened signal. Simulation results show the great potential of the proposed method.