Narrowing provides a complete procedure to solve equations modulo confluent 
and terminating rewriting systems. But it seldom terminates. This paper 
presents a method to improve the termination. The idea consists in using a 
finite graph of terms built from the rewriting system and the equation to 
be solved, which helps one to know the narrowing derivations possibly 
leading to solutions. Thus, the other derivations are not computed. This 
method is proved complete. An example is given and some improvements are 
proposed.