This paper introduces a deterministic algorithm for solving an instance of the Subset Sum Problem based on a new method entitled the Bipartite Synthesis Method. The algorithm is described and shown to have worst-case limiting performance over similar to the best deterministic algorithms achieving run time complexity on the order of O(2^0.5n). This algorithm is representative of a more expansive capability that might convey significant advantages over existing deterministic or probabilistic methods, and it is amenable to blending with existing methods. The method introduced can be applied to a variety of decision and optimization problems.