Network decomposition has been proven to be one of a large set of problems termed “NP Complete” (nondeterministic polynomial) (Gundersen and Hertzberg, 1982). NP complete problems have no known method of solution better than trying all the possibilities, nor, according to most mathematicians, is any superior method likely to be found (Wasserman, 1989). Because such an exhaustive search is generally impractical for large networks, heuristic methods have been applied to find solutions that are acceptable if not optimal. A new heuristic strategy for sequencing of calculation of the unit modules in sequential modular flowsheeting and determining the tear streams is presented. The method neither involves the use of the signal flow graph nor information on cycles in the network. The algorithm has been tested on several problems collected from chemical engineering literature and includes the very complex graph of a heavy water plant suggested as a benchmark problem by Gundersen and Hertzberg (1982). The proposed algorithm finds the optimal number of tears for twelve of the test problems, while the number of tears found for the remaining two problems is only one more than the optimum value. For large problems, which are not easily handled by optimal tearing routines, this method can serve as an upper bound algorithm in a branch and bound strategy. © 1992, Taylor & Francis Group, LLC. All rights reserved.