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With the increasingly extensive applications of the new emerging video coding standard H.264, it inspires an urgent need to transcode the widely available MPEG-2 compressed video to H.264 format. In this paper, we investigate the issues on transcoding MPEG-2 into H.264 in transform domain with consideration of drift error due to the mismatch of motion compensation, and propose a transform domain solution to transcode MPEG-2 into H.264. We first analyze two major kinds of drifting error resulting from the mismatch of motion compensation: interpolation error and quantization error. The former is caused by the difference between the interpolation filters adopted in these two standards, thus very unique to the transform domain transcoding from MPEG-2 to H.264. Furthermore, it is identified as the dominant factor of the video quality degradation, especially in the case of small quantization parameter at high bit-rate, by extensive experimental results. As a major contribution of this paper, the close form of interpolation error is derived from transform domain. We then proposed the transcoding scheme based on quantization error drifting compensation and Interpolation error drifting compensation. Experimental results show that the proposed transform domain transcoding scheme achieves very promising performance in terms of low computational complexity and high transcoded video quality. Most importantly, its peak signal-to-noise ratio is very close to the cascaded transcoding architecture with time-consuming decoding and recoding process in pixel domain.