This note addresses the problem of identifying the pinch defining streams and the pinch point during grassroots heat exchanger network (HEN) design for problems in which the composite curves are discontinuous. We show that there can exist a logical lower bound on the heat recovery approach temperature (DeltaT(min)) for such problems, thereby reducing the range over which targeting needs to be done. Direct application of the Problem Table Algorithm (Linnhoff-March Limited, Knutsford, UK. Process Integration: Part I(a), December 1992) does not determine this lower bound and can also result in the identification of pinch points at which the pinch design rules cannot be directly applied. We present here an example of such a situation and explain how these special cases can be handled.