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In the upcoming H.264, intra-prediction with block sizes of 4×4 and 16x16 is used to compress I-frame. However, there are 9 or 4 candidate modes for the 4x4 or 16x16 intra-prediction. The full search algorithm to choose the modes is computationally expensive. In this paper, we suggest an efficient intra-prediction (EIP) algorithm based on early termination, selective computation of highly probable modes, and partial computation of the cost function. The proposed EIP reduces the complexity considerably while maintaining similar PSNR and bit rate.