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Pattern matching is a powerful tool for querying sequence patterns in the biological sequence databases. The remarkable increase in the number of DNA and proteins sequences has also stimulated the study of many pattern matching algorithms. To further raise the performance of the pattern matching algorithm, a fast exact algorithm (called BRFS) is presented. It bases on the method of FS algorithm and absorbs the idea of BR algorithm during the pattern matching, thus reaches the best shift distance and improves the performance. The best, worst and average cases in time complexities of the new algorithm are also discussed. The experimental results show that the new algorithm is faster than other compared algorithms for small alphabets and long patterns, so the proposed algorithm is quite applicable for pattern matching in biological sequences.