Abstract Energy savings in existing plants usually have positive economic and environmental impacts. Mathematical approaches to heat-exchanger network (HEN) retrofit are complex and do not guarantee identification of the global optimum. Thanks to its simplicity the pinch-based approach is widely used, even though difficulties for its adaption to HEN retrofit are encountered. This paper presents the concepts supporting a new analysis method for HEN retrofit. Energy is conserved and degraded through heat exchanges and process operations. Reducing heat consumption implies a reduction in the flow rate of heat transferred from the heating utility through the existing heat exchanger network until rejected to the environment. This progressive transfer of heat in the existing heat exchanges from the heating utility to the environment is not explicitly analyzed in the present approaches for HEN retrofit. For the first time, the set of modifications necessary to reduce the heat consumption is made explicit; this set is represented by a “bridge”. An energy transfer diagram to identify bridges and a network table to easily identify and evaluate bridges are proposed. A method to enumerate the bridges is described. The principle of bridge improves the comprehension about the problem of HEN retrofit, and its application results in a significant search space reduction; this reduction is all the more so useful since this problem is non-deterministic polynomial-time hard. A global procedure for HEN retrofit and case studies are presented in a second paper.