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 [3], [4] and another simpler technique called the one-at-a-time search [3]. 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 [1], and a modified version of it [2], for motion compensated prediction [5].