The differentiation of the quaternary reciprocal system Li, K, Ca, Ba parallel to F, WO4 was performed based on the graph theory using special software. Stable and metastable complexes of the system were found using a matrix of reciprocal pairs of salts. For the first time, by a set of physicochemical analysis methods (differential thermal, visual polythermal, and X-ray powder diffraction analyses), based on the method of thermal analysis of successive projections of the composition polytope, the quaternary system LiF-K2WO4-CaF2-BaF2-BaWO4, which is a stable complex of the quaternary reciprocal system Li, K, Ca, Ba parallel to F, WO4, was studied and the coordinates of invariant points were determined.