An innovative technique for estimating displacement of motion vector within small blocks with minimum mean of absolute difference is presented. An efficient algorithm for searching the direction of displacement has been described. The motion compensation is applied for analysis and design of a hybrid coding scheme and the results show a factor of two gain at low bit rates. The algorithm uses circular 2-D Logarithmic search [CLS] technique for best prediction of minimum distortion block. The search area is continuously reduced by a factor of 2 each time search for best motion vector takes up a new direction with the number of points to be searched for each iteration, decreasing continuously than the first iteration. Experimental results prove the proposed CLS Algorithm has a speed gain of more than 30% over diamond search [DS] algorithm for finding large motion vectors. The approach has been successfully tested under for standard sets of 6 video sequences. An illustrious comparison with parameters such as increase in SIR (%) has been drawn between our algorithm and DS algorithm.