In this paper, we propose a new algorithm for enforcing relational consistency on every set of k constraints of a finite Constraint Sat- isfaction Problem (CSP). This algorithm operates by filtering the constraint while leaving the topology of the graph unchanged. We study the resulting relational consistency property and compare it to existing ones. We evaluate the effectiveness of our algorithm in a search procedure for solving CSPs and demonstrate the appli- cability, effectiveness, and usefulness of enforcing high levels of consistency.