This paper presents a unifying approach for a reliable calculation of all azeotropes and pinch points for homogeneous and heterogeneous non-reactive mixtures. The approach builds on a reformulation of the pinch-equation system and an efficient continuation algorithm including bifurcation analysis. The calculation of azeotropes is based on an analogy of univolatility curves and the pinch branches for pure component products. The resulting method can efficiently and reliably calculate all homogeneous and heterogeneous non-reactive azeotropes. The only exception would be the existence of isolated univolatility curves inside the composition space, which to the best knowledge of the authors has never been reported. Since the method can further determine the pinch branches and pinch points based on the knowledge of the azeotropes, it presents a self-contained method for calculation of the most important information on nonideal multicomponent mixtures to support process synthesis. The application of the method is illustrated by means of several complex mixtures.