This research proposes a new graphical method for the analysis of heat recovery systems, applicable to both phases of grassroots and revamping. The new graphical method is based on plotting temperatures of process hot streams versus temperatures of process cold streams. A new graph is constructed for representing existing preheat trains. For a given preheat train, each existing exchanger is represented by a straight line, whose slope is proportional to the ratio of heat capacities and flows. Further, the length of each exchanger line is related to the heat flow transferred across this exchanger. This new graphical representation can easily identify exchangers-across-the-pinch, Network Pinch, pinching matches and improper placement of fuel consumption. Furthermore, such a graph can recognise promising modifications to improve the energy performance and hence less fuel and cooling water requirement. Graphs developed in this work can be used to analyse the energy performance of existing networks with respect to energy targets. They can also be used in junction with the background process to modify basic designs or existing network for better energy integration opportunities and minimum fuel demands.