This paper explores the representation of bivariate distributions in terms of their bivariate uniform trsnslates. It is shown that this natural rapresentation in terms of bivariate distributions whose marginals are uniform allows us to study easily cartain properties of bivariate distributions. We demonstrate the invariance under translation of some well-known measures of dependence. Finally it is shown how this approach allows us to find new bivarariate distributions and simpler derizations of known bivariate distributions.