This paper presents a new method for handling removable discontinuities in non-convex mixed integer non-linear programming (MINLP) models for chemical process synthesis and design. First, the occurrences of different kinds of discontinuities in design equations are discussed. Then methods so far developed for handling discontinuities in an MINLP design environment are summarized. In the main part of the paper, a new method is presented for handling removable discontinuities. Our new method is compared to five conventional literature methods applied to three mass exchange network synthesis problems of different size, where the Kremser equation is used for calculating the number of equilibrium stages. In addition, a heat exchange network synthesis problem is considered where the logarithmic mean temperature difference is calculated rigorously. Our method proved to be much faster than the other methods examined and shows less sensitivity to the change of initial values in terms of optimal objective function value and solution time.