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We propose a blind upmixing method for stereo music signals that utilizes multi-step linear prediction and decomposes the input signals into reverberation and the dereverberated signals. The proposed method is directly motivated by our previously proposed dereverberation algorithm that was shown to dereverberate speech signals well. In this paper, we first analyze the behavior of the multi-step linear prediction and investigate the reverberation reduction/extraction strategy using a stereo music signal model. Based on the analysis, we show that the proposed method can perform a dereverberation and reverberation extraction based on the stereo music signal, and achieve an efficient blind upmix of stereo music by assigning its dereverberated signal to the front channels and extracted reverberation to the rear channels. In the experiment, we apply the proposed upmixing method to real stereo music signals, and confirm its effectiveness with an objective evaluation and a preference test.