A new method for describing the phase equilibria of a multicomponent system in the matrix form is proposed. A system of equations which describes a higher order phase diagram consists of: polynomial expressions correspond to the hypersurfaces representing the phase boundaries of one-phase regions and the relationships expressing the phase equilibria between phases. As an example, the results of liquidus surface estimation of quasi-ternary InBi-Sn-Pb alloys are presented. For liquidus surface representation in this system three binary subsystems and only few experimental data on ternary alloys are used. The method can be ap¬plied to the phase diagrams as a whole or its parts.