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To reduce the amount of computations for a full search (FS) algorithm for fast motion estimation, we propose a new and fast FS motion estimation algorithm. The computational reduction of our FS motion estimation algorithm comes from fast elimination of impossible motion vectors. We obtain faster elimination of inappropriate motion vectors using efficient matching units from localization of a complex area in image data. In this paper, we show three properties in block matching of motion estimation. We suggest two fast matching scan algorithms: one from adaptive matching scan and the other from fixed dithering order. Experimentally, we remove the unnecessary computations by about 30% with our proposed algorithm compared with the conventional fast FS algorithms.