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In hybrid moving-picture coding schemes, motion estimation is conducted in two stages, one at integer pixel accuracy and the other at subpixel accuracy. In very low bit-rate coding, some fast motion-search algorithms are able to decrease their search points to about ten pixels at the integer pixel search stage. There remains, however, a need to study fast computing for the subpixel motion estimation. A novel, fast-search algorithm using parabolic prediction is proposed in this paper particularly for the half-pixel motion vector estimation. It needs to check only three half-pixels rather than the eight pixels, which are used in the full half-pixel motion search scheme (FHPS). Experimental results show that this algorithm preserves the image quality and has little influence on the bit-rate when compared to that of the referenced FHPS strategy.