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The problem of redundancy among test sequences derived from different FSM-based test coverage criteria often emerges in practice, resulting in the increasing of test cost of software. To solve this problem, a novel approach by way of string matching to eliminating redundancy among test sequences is presented in the paper. Four types of redundancies of test sequences are described and the corresponding reduction rules are also designed. To ensure the effectiveness of redundancy reduction, a transformation rule to convert the ineffective test segments into the effective test sequences is proposed. And then a novel algorithm for redundancy reduction is designed and implemented with Java language. Finally an example is illustrated for the achievement of our approach. Comparing with the existing researches about redundancy reduction, our approach not only eliminates most redundancies among test sequences, but also promotes the application of FSM-based test coverage criteria in practice.