A mixing rule recently developed by Twu and Coon [C.H. Twu, J.E. Coon, CEOS/A(E) mixing rules constrained by the vdw mixing rule and the second virial coefficient, AIChE J. 42 (1996) 3212-3222] is extended to incorporate the UNIFAC group contribution method into an equation of state for the prediction of phase behavior of highly non-ideal systems over wide ranges of temperature and pressure. The mixing rule developed by Twu and Goon reduces to the van der Waals mixing rule. The Helmholtz excess free energy function with respect to a van der Waals fluid at infinite pressure has been related rigorously to the Helmholtz excess free energy at zero pressure. This extension of the Twu-Coon Mixing Rule goes gracefully from the classical van der Waals one-fluid mixing rule for non-polar fluids needed in the refining and gas processing industries to a mixing rule combining excess free energy models at low pressure with equations of state for the strongly polar systems found in the chemical industries. When the UNIFAC group contribution method is incorporated, the mixing rule becomes totally predictive, The completely predictive equation of state is shown to give accurate results for systems for which the UNIFAC model is in agreement with the experimental activity coefficients at low pressure. The UNIFAC-incorporated mixing rule provides a simple way to extend the UNIFAC group contribution method to high temperatures and pressures.