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Regression testing is a critical activity which occurs during the maintenance stage of the software lifecycle. However, it requires large amounts of test cases to assure the attainment of a certain degree of quality. As a result, test suite sizes may grow significantly. To address this issue, Test Suite Reduction techniques have been proposed. However, suite size reduction may lead to significant loss of fault detection efficacy. To deal with this problem, a greedy algorithm is presented in this paper. This algorithm attempts to select a test case which satisfies the maximum number of testing requirements while having minimum overlap in requirements coverage with other test cases. In order to evaluate the proposed algorithm, experiments have been conducted on the Siemens suite and the Space program. The results demonstrate the effectiveness of the proposed algorithm by retaining the fault detection capability of the suites while achieving significant suite size reduction