This paper combines mathematical optimization techniques with a better understanding of the retrofit problem, based on thermodynamic analysis and practical engineering, to produce a systematic procedure capable of efficiently solving industrial size retrofit problems. The major characteristic of the approach presented is that it offers a systematic and automatic method for the retrofit design of heat exchanger networks (HENs), combined with a facility for meaningful user interaction. The new procedure employs a two-stage approach for retrofit HEN design : The first stage is the diagnosis stage, during which a minimum number of promising HEN topology modifications is obtained which enables a desired heat recovery target to be achieved. In the second stage, the optimization stage, the HEN obtained after implementation of the modifications is optimized using non-linear optimization techniques to minimize the cost of additional surface area employed. It has been observed that heat recovery in a HEN is thermodynamically limited by certain exchanger matches unavoidably tending to a zero degree temperature approach as the heat recovery increases. These exchanger matches, which are termed as pinching matches, act as a bottleneck to heat recovery in the HEN. To increase the potential for heat recovery beyond the limits caused by the pinching matches, the network topology must be altered by repiping of exchangers, addition of new exchanger matches or creation of stream splits. Based on the above observation, the diagnosis stage is made up of two steps. In the first step the HEN bottleneck is identified, and in the second step a mixed integer Linear programming (MILP) formulation is used to select a single modification which will best overcome the identified bottleneck. These two steps are repeated in a loop to yield the required set of promising topology modifications.