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Every day much information is transmitted in such forms as images, sounds and texts. These data of images and sounds are particularly large and need an efficient compression method. The LZ77 algorithm is one of the most effective compression algorithms. In this paper, two new algorithms are given in order to improve the performance of the original LZ77 algorithm. One is to check whether it can get the longest match before matching, and the other is to save the longest common prefix of the adjacent strings in the list to improve the efficiency. It is proved that the two new algorithms achieve the expectation after a comparative analysis with other versions of the LZ compression algorithms.