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 elimination process is continued through the use of Shannon decomposition. Numerical results show that the performance of this algorithm is significantly superior to that of a previous algorithm proposed by the authors