The consistency of reciprocal preference relations is studied. Consistency is related with rationality, which is associated with the transitivity property. For fuzzy preference relations many properties have been suggested to model transitivity and, consequently, consistency may be measured according to which of these different properties is required to be satisfied. However, we will show that many of them are not appropriate for reciprocal preference relations. We put forward a functional equation to model consistency of reciprocal preference relations, and show that self-dual uninorms operators are the solutions to it. In particular, Tanino's multiplicative transitivity property being an example of such type of uninorms seems to be an appropriate consistency property for fuzzy reciprocal preferences.