Many program analysis techniques depend on capturing the control dependencies of the program. Most existing control dependence algorithms either compute intraprocedural control dependencies only, or they compute control dependence relations that are not precise in general including nonterminating systems. Weak control closure (WCC) subsumes all known nontermination insensitive control dependence relations, including those that are appropriate for nonterminating systems. In this paper, we provide the first formal development of an algorithm to compute the WCC for interprocedural programs capturing the weak form of interprocedural control dependencies. The method is widely applicable due to the generality of WCC. Theorems on the theoretical results of soundness, precision, and the worst-case complexity of our method are also included. We have compared our algorithm with a WCC computation algorithm based on a state-of-the-art interprocedural control dependence computation algorithm. The latter algorithm loses soundness, and we improve the precision by 15.21% on all our experimental benchmarks. This empirical evidence suggests that our algorithm is more effective for any client application of WCC requiring interprocedural program analysis.