We consider the disassembly sequencing problem subjected to sequence dependent disassembly costs. Because most of the available methods that deal with such problems rely on metaheuristic and heuristic methods, it is desirable to have exact methods available that can at least be applied to medium sized problems to determine if the heuristically obtained solutions are acceptable or not. The conventional integer linear programming (ILP) approaches become unmanageable even for modest product complexity cases. In this paper, we propose an iterative method that repeatedly solves a binary integer linear programming (BILP) problem. The method converges quickly for medium sized problems. We use the proposed method to solve a cell phone problem from practice, consisting of 25 components that are represented, according to a set of precedence relationships, via a disassembly precedence graph.