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With the remarkable increase in the number of DNA and proteins sequences, it is necessary to study pattern matching in querying sequence patterns in the biological sequence database. To further raise the performance of the pattern matching algorithm, a fast hybrid algorithm (called ZTFS) is presented. It bases on the basic method of Zhu-Takaoka algorithm and absorbs the idea of fast search during the pattern matching to reduce the number of comparisons, and thus improves the performance. The best, worst and average cases in time complexities of the algorithm are also outlined. The experimental results show that the new algorithm works better than other compared algorithms, especially in case of small alphabets such as nucleotides sequences, and thus the proposed algorithm is more suitable for exact pattern matching in biological sequences.