The available algorithmic methods often fail to yield with certainty the global optima in solving even a relatively simple class of separation-network synthesis problem for which the cost functions are considered to be linear. This is attributable to two complications; firstly the super-structures on which the solutions are based are incomplete; and the secondly, the mathematical programming models derived for the problems are unnecessarily cumbersome. To circumvent these complications, a novel method is proposed here to generate the complete super-structure and the corresponding mathematical programming model necessary for the separation-network synthesis problem with linear cost function. The efficacy of the proposed method is demonstrated by re-examining Four published problems for which the optima obtained are claimed to be global. For all the problems re-examined, the costs of the solutions resulting from the present method are the same or as much as 30% lower than those of the published solutions.