We present a general algorithm for determining all intra fact type uniqueness constraints in a fact type with n roles. For Fact Oriented Methods of information modeling that work with elementary fact types, a top-down ap-proach is shorter than a bottom-up approach for fact types with more than two roles. The algorithm is shorter (in terms of the number of tests to be performed) than the one published earlier in our book on FCO-IM. For its most important steps, we prove that no shorter algorithm exists.