In a recent paper, Campbel (1994) shows that if a choice correspondence satisfies Arrow8217;s choice axiom then it has a complete, reflexive and transitive rationalization, even if the domain does not include any set with fewer then m members, where m is a given positive integer. The purpose of this paper is to provide a simpler proof (than the one provided by Campbell) of the same result when the choice correspondences are single – valued i.e., the case of choice functions. In such a situation Arrow's choice axiom is formally equivalent to Nash's Independence of Irrelevant Alternatives assumption.