A new method is proposed for obtaining the transformations that enable the application of the McCabe-Thiele method to the case when the saturated liquid and vapor enthalpy curves are straight but non-parallel lines. A rigorous framework which has a sound physical and mathematical basis and which brings into greater focus the central importance of the parallel enthalpy lines assumption to the McCabe-Thiele method is developed. Explicit expressions for the transformations of not only the composition and flow rate but also enthalpy are obtained. A detailed comparison of the methods adopted in this work with those in the literature is made. The specializing conditions under which the transformations in the literature emerge from a more general set are found. Extension to multi-component mixtures is demonstrated. It is shown that the framework presented here provides a rational basis for the prescriptions obtained from the "fictitious molecular weight" concept. Further, contrary to claims in the literature, the applicability of that concept to multi-component mixtures is demonstrated. Finally, the fresh perspective gained from the framework is used to widen the scope of its applicability and generalization to other separation processes such as extraction, adsorption and leaching is undertaken. © 2008 Elsevier Ltd. All rights reserved.