We present a simple and fast algorithm to test the thermodynamic stability and determine the necessary chemical environment for the production of a multiternary material, relative to competing phases and compounds formed from the constituent elements. If the material is found to be stable, the region of stability, in terms of the constituent elemental chemical potentials, is determined from the intersection points of hypersurfaces in an (n-1)-dimensional chemical potential space, where n is the number of atomic species in the material. The input required is the free energy of formation of the material itself, and that of all competing phases. Output consists of the result of the test of stability, the intersection points in the chemical potential space and the competing phase to which they relate, and, for two- and three-dimensional spaces, a file which may be used for visualization of the stability region. We specify the use of the program by applying it both to a ternary system and to a quaternary system. The algorithm automates essential analysis of the thermodynamic stability of a material. This analysis consists of a process which is lengthy for ternary materials, and becomes much more complicated when studying materials of four or more constituent elements, which have become of increased interest in recent years for technological applications such as energy harvesting and optoelectronics. The algorithm will therefore be of great benefit to the theoretical and computational study of such materials. © 2013 Elsevier B.V. All rights reserved.