For a heat exchanger network that contains more than the minimum number of units, it is often required to simplify the network by removing extra units. A new method is proposed to find the best units for breaking loops involved in the network. The energy penalty incurred by deleting a unit from a loop depends not only on the heat loads of all units but; also on the structure of the network. To take into account the effects of heat; loads and interactions of units on energy relaxation, the constrained units that cannot absorb any transferred energy and the redistribution of Delta t(min) are discussed. The constrained units make the evaluation of energy penalties of some units simple and straightforward. When the redistribution of Delta t(min) caused by deleting a unit is examined, the lower bound of the energy penalty of the unit can be easily estimated. When the lower bound is compared with the heat loads of other units, it can be decided whether the unit should be deleted or not. The proposed method is reliable and efficient. It considers effects of both the heat loads and the interactions of units and avoids calculations of the accurate energy penalties of all units. A common testing example is used to demonstrate the effectiveness of the proposed method.