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Fast block-matching motion estimation algorithms for video compression are in real-time video conference applications. Three-step Search (TSS) and other fast search algorithms such as Diamond Search (DS), Cellular Search (CS), New Cross Diamond Search (NCDS), Fast Cellular Search (FCS) have been proposed to reduce the computation time instead of the full-search block-matching algorithm in video compression applications. To reduce more computational complexity and maintain the quality of compressed video, a novel algorithm based on the spirit of CS is proposed and named New Cellular Search (NCS). This proposed algorithm has two search patterns in horizontal and vertical directions with different switching strategy to reduce the computation time. The experimental results are shown that this proposed algorithm is superior to some fast search algorithms.