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In the upcoming H.264 advanced video coding standard, intra-prediction for each 4×4 block is used to compress I-frames. However, the full search algorithm to choose one of the 9 prediction modes is computationally expensive. We propose a fast intra-prediction mode selection (FIPMS) method based on partial computation of the cost function, early termination and selective computation of highly probable modes. The proposed FIPMS can reduce the complexity considerably while maintaining similar PSNR and bit rate.