This paper describes an algorithm for the efficient solution of large systems of Boolean equations. The algorithm exploits the fact that, in some cases, the composition operation of Boolean functions represented by BDD's can be performed in a very efficient manner. Thus, the algorithm tries to eliminate as many variables and equations as possible through function composition. When the system can no longer be reduced in this way, the eliminationprocess is continued through the use of Shannon decomposition. Numerical results show that the performance of this algorithm is significantlysuperior to that of a previous algorithmproposed by the authors.