Congruence closure on ground equations is a well-established, efficient algorithm for deciding ground equalities. It computes an explicit representation of the ground equivalence classes on the basis of a set of ground input equations. Then equalities are decided by membership. We generalize the ground congruence closure algorithm to non-ground equations. The algorithm also computes an explicit representation of all non-ground equivalence classes. It is terminating due to an a priori bound on the term size. By experiments we compare our new algorithm with ground congruence closure.