A matrix representation of separation for production of mixed products with one feed is extended to represent general distillation processes which involve separating several multicomponent feeds into several multicomponent products. A heuristic procedure is also presented for the synthesis of sequences of simple, sharp split distillation columns with bypass through operating the Separation Product Matrix (SPM) representing products. In the heuristic procedure the influence of the current separation and the successive separations on separation cost are considered simultaneously. Three examples are given to show the synthesis procedure.