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A computationally simpler and effective method is proposed for estimating motion in a video sequence. The paper outlines a search technique based on conjugate directions ,  and another simpler technique called the one-at-a-time search . Based on the comparison of the two methods, the latter technique is adopted as the basis for further research. The adopted technique is compared with brute force search, existing 2-D logarithmic search , and a modified version of it , for motion compensated prediction .