The concept of maximization of entropy flux as a design tool for a network of heat exchangers is further expanded on. The optimum network is equivalent to a network of counter flow heat exchangers connected in series, where hot and cold streams are added to, or removed from the respective streams of the heat exchangers at locations where the temperatures of the streams flowing in the heat exchanger have reached the temperatures of the streams that are to be added or removed. This ideal network of heat exchangers, where the fluids are mixed together, can be realized in practice through a combination of other heat exchangers arranged in parallel and series. This methodology identifies the optimum network easily, without the need for using complicated optimization algorithms. An improved systematic approach is presented through a step by step example is to show how to arrive at the network with the minimum area.