This paper is concerned with finding timing-independent false paths that cannot be sensitized under any signal arrival time condition in integrated circuits. Existing techniques regard a path as a true path as long as a vector pair can be found to sensitize it. This is rather pessimistic since such a path might be activated only with illegal states in the circuit and hence it is actually functionally-unsensitizable. In this paper, we develop novel techniques to take the above issue into consideration when identifying false paths, which facilitates us to find much more false paths than conventional techniques. Experimental results on benchmark circuits demonstrate the effectiveness of the proposed methodology.