Recently efficient hardware architectures were proposed for the fast execution of H.264/AVC intra prediction. However, these architectures waste hardware resources because intra predictions and reconstructions of sixteen 4x4 blocks in one macroblock are serialized. This paper proposes an efficient pipelining method for the intra predictions and reconstructions of the 4x4 blocks. A new processing order is proposed to reduce dependencies between consecutively executed blocks Thus, pipelined executions of these thirteen blocks speed up the execution time by 41% with a negligible drop-off of the compression efficiency when compared to the non-pipelined execution of the order in the JM reference software. Parallel executions of the intra prediction of Luma 4x4 blocks and the intra predictions of Luma 16x16 blocks and Chroma 8x8 blocks further reduce the execution time. When compared with the best previous work [1], the execution time is reduced by 13%.