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Regression test selection is to select a subset of existing tests to run, so as to identify the possible faults in the modified program. A promising regression test selection technique needs to be safe, that is, to select tests from the original test suite that can expose faults in the modified program under controlled regression testing. Existing safe regression test selection techniques however may rerun some tests that do not expose faults. To address this problem, we present in this paper a new regression test selection technique based on program dependence graphs of a program and its modified version. Comparing with previous techniques, our technique can eliminate some unnecessary tests to rerun. We show the validity and feasibility of our approach through a running example.