Advantage is taken of an unused potential which lies in the evolutionary development method for heat exchanger networks (HEN) proposed by Linnhoff and Flower to construct an algorithm which reduces recursively the number of units of a given HEN problem. As a result, all networks are generated that fulfill the heating and cooling requirements of the problem and whose number of units cannot be further reduced. Among the solutions obtained, those are selected which satisfy the condition of minimum permissible temperature driving force. A C++ implementation of the algorithm has been applied to a number of problems taken from the literature.