In this paper, we propose a new and complete method based on narrowing for solving equations in equational theories. This method is complete in the sense that it gives all the solutions. It is a combination of basic narrowing, which is not obvious, because their naïve combination is not a complete method. We show that it is more efficient than the existing methods in many cases, and for that establish commutation properties on the narrowing. It provides an algorithm that has been implemented as an extension of the software REVE.
