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Discrete cosine transform (DCT) is the orthogonal transform that is most commonly used in image and video compression. The motion-compensation residual (MC-residual) is also compressed with the DCT in most video codecs. However, the MC-residual has different characteristics from a nature image. In this paper, we develop a new orthogonal transform-rotated orthogonal transform (ROT) that can perform better on the MC-residual than the DCT for coding purposes. We derive the proposed ROT based on orthogonal-constrained L1-Norm minimization problem for its sparse property. Using the DCT matrix as the starting point, a better orthogonal transform matrix is derived. In addition, by exploring inter-frame dependency and local motion activity, transmission of substantial side information is avoided. The experiment results confirm that, with small computation overhead, the ROT is adaptive to change of local spatial characteristic of MC-residual frame and provides higher compression efficiency for the MC-residual than DCT, especially for high- and complex-motion videos.