This article addresses the problem of minimizing the number of heat exchangers for heat recovery as well as the number of mixing and splitting junctions within water networks while maintaining the energy targets determined by the classical pinch analysis. A new systematic approach is proposed to eliminate the kink points and linearize the composite curves. This is based on a systematic strategy that indicates how to mix and split the water streams in order to modify the shape of the initial composite curves. A new graphical thermodynamic rule that avoids the deterioration of energy targets while minimizing the number of heat transfer units as well as the mixing and splitting network complexity has been formalized. This rule permits the control of the procedure of mixing and splitting on the T-H diagram in order to guarantee the pre-established targets. The proposed approach can be used for either the manual design of heat recovery within water networks or the building of a superstructure with a limited number of feasible design options.