Consistency properties and algorithms for achieving them are at the heart of the success of Constraint Programming. In this paper, we study the relational consistency property R(∗,m)C, which is equivalent to m-wise consistency proposed in rela- tional databases. We also define wR(∗,m)C, a weaker variant of this property. We propose an algorithm for enforcing these properties on a Constraint Satisfaction Problem by tighten- ing the existing relations and without introducing new ones. We empirically show that wR(∗,m)C solves in a backtrack- free manner all the instances of some CSP benchmark classes, thus hinting at the tractability of those classes.