A thermodynamically orientated method is presented for the synthesis of heat exchanger networks. With this method, the problem is solved in two stages. In the first stage, preliminary networks are generated which give maximum heat recovery. In the second stage, the most satisfactory final networks are evolved using the preliminary networks as starting points. In this paper, emphasis is given to the synthesis of the preliminary networks. Two four-stream examples are solved. In Part II, emphasis will be given to the synthesis of final networks.