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In most reversible compressed video watermarking schemes, there is a particular problem that the distortion of image quality will be spread and accumulated. In this paper, we analyze the problem of distortion drift caused by reversible watermarking in compressed video, and then a lossless drift compensation scheme for compressed video is proposed. The experimental results show that the lossless drift compensation method we propose in this paper will significantly improve the visual quality of embedded compressed video, while allowing recovering the standard encoded video exactly. In addition, the lossless drift compensation approach does not depend on the specific embedding and extraction of reversible watermark, and it also can be used in the video reversible watermarking based on other compression standards such as H.264.