Except for the trivial case of one-component systems, the conventional Schreinemakers phase stability analysis in invariant systems is shown to be thermodynamically and stoichiometrically inconsistent in that the partition of the stability relations into contributions coming from univariant subsystems is formulated only qualitatively. Although the stability relations in invariant systems are essentially additive (i.e., the stability relations in invariant system may be partitioned into a sum contributions coming from univariant subsystems), the quantitative form of this partition has never been considered. On the basis of a new approach to the stability of chemical species in multiple chemical reaction systems that has been recently developed by us (Fishtik, I. J. Phys. Chem. B, 2005, 109, 385 1), we show how the stability relations in invariant systems may be uniquely partitioned into contributions coming from univariant reactions. This finding provides a simple algorithm for the construction of various types of thermodynamically consistent stability diagrams.