Recent insights into the nature of optimal separation-networks indicate a need to develop a rigorous technique capable of generating the optimal solution of a separation-network synthesis (SNS) problem. In principle, an SNS problem can be solved if an exact super-structure is available. Hitherto, no method has been established for generating such a super-structure when multiple feed-streams are involved. Even when a super-structure is complete, the corresponding mathematical-programming problem may not be solvable if it is unnecessarily complex. Thus, the exact super-structure should be as simple as possible. The present paper proposes an algorithm for generating an exact super-structure for the following class of SNS problems: multiple feed-streams and multicomponent product-streams where the cost function of each separator is linear with a fixed- charge. It has been proved that the super-structure generated always includes the optimal separation-network of this class of problems and that the super-structure does not include unnecessary operating units. The proposed method have been demonstrated by successfully solving several problems.