H. Minc has constructed an upper bound on the permanent of any relation on a finite set. In this paper the permanent of any transitive relation on a finite set is calculated. The work in part is based upon the interpretation of a reflexive, transitive relation as a finite topology. The relationship to (finite) Borel fields is discussed briefly. In an example it is shown how results here may be combined with Minc’s inequality to produce an improved upper bound on the permanent of any relation.