In this paper, a new global optimization approach for the synthesis of heat exchanger networks is presented. The Synheat model by [Comp. Chem. Eng. 1 (1990) 1165] uses a promising superstructure that includes the most common heat exchanger structures, and optimizes utility costs, the number of units and heat exchanger areas simultaneously. With some minor modifications of the model, it is possible to apply a new global optimization strategy to the problem. The heart of the strategy is to convexify signomial terms, and create approximate convexified subproblems. If the Synheat model is extended in an appropriate way, the isothermal mixing assumption can be removed. Applying the new global optimization strategy to the model allowing non-isothermal mixing makes it possible to find truly optimal network configurations for the case of constant heat-capacity flow rates and heat transfer coefficients. Some examples to illustrate the global optimization strategy and to illustrate that the Synheat model can exclude optimal configurations due to the isothermal mixing assumption are also given in this paper.