For an N-component separation, distillation systems with less than N-1 columns have the potential to save both energy and capital costs compared to the conventional simple column configurations where N-1 columns are employed. Recently, for four-component separations, Kim and Wankat [J.K. Kim, P.C. Wankat, Quaternary distillation systems with less than N-1 columns, Ind. Eng. Chem. Res. 43 (2004) 3838-3846] analyzed a few distillation systems with less than N-1 columns and presented tentative heuristics for selecting the best configuration among those studied. In this paper, a method for the systematic synthesis of all the distillation systems with less than N-1 columns is presented. Starting from the simple column configurations for the separation of an N-component mixture, a four-step procedure is formulated which systematically generates all the possible distillation systems with less than N-1 columns. First, the subspace of the possible thermally coupled configurations corresponding to the simple column configurations is generated. Then, the subspace of the possible thermodynamically equivalent structures corresponding to the thermally coupled configurations is produced. Finally, the subspace of the distillation systems with less than N-1 columns corresponding to the thermodynamically equivalent structures is achieved. The method is simple, easy-to-use and can systematically synthesize all the possible distillation systems with less than N-1 columns. It is shown that a large number of such distillation systems with less than N-1 columns have been achieved for the first time. This constitutes a complete new subspace. A case study shows the advantages of such distillation systems with less than N-1 columns over the other schemes. The significance to formulate a complete subspace of such systems is that, on the one hand, it can be used to further develop more reliable heuristics by simulations. On the other hand, an optimization framework can be formulated to screen the possible optimal system for a specific application. (c) 2008 Elsevier B.V. All rights reserved.