It has been shown previously that a logic circuit often contains a large number of logical paths that need not be tested to verify the timing behavior of the circuit, if the other paths are robustly tested. These paths are called robust dependent. A subset of the robust dependent paths are the functionally unsensitizable paths. This paper proposes a method for efficiently identifying both types of paths. The proposed procedure uses local circuit analysis to keep the run time relatively low, and relatively independent of the number of paths in the circuit. The method may not identify all the paths that are robust dependent or functionally unsensitizable, however, experimental results show that the numbers it finds are comparable, and sometimes even higher than those found by other methods. The procedure can be applied to circuits that cannot be handled by other methods.