Software testing and retesting occurs continuously during the software development lifecycle to detect errors as early as possible. The sizes of test suites grow as software evolves. Due to resource constraints, it is important to prioritize the execution of test cases so as to increase chances of early detection of faults. Prior techniques for test case prioritization are based on the total number of coverage requirements exercised by the test cases. In this paper, we present a new approach to prioritize test cases based on the coverage requirements present in the relevant slices of the outputs of test cases. We present experimental results comparing the effectiveness of our prioritization approach with that of existing techniques that only account for total requirement coverage, in terms of ability to achieve high rate of fault detection. Our results present interesting insights into the effectiveness of using relevant slices for test case prioritization.