In this paper, a novel branch and bound algorithm based on the idea of Horst (Math Program. 1976, 10, 312) was developed to minimize the tangent plane distance function (TPDF) of the stability analysis problem where nonideal liquid phases are described by the UNIQUAC activity coefficient equation. Some simple transformations were used to construct the DC (i.e., difference of two convex functions) programming of TPDF that does not rely on any newly introduced parameters except the inner ones of the UNIQUAC equation. A compact partition of the feasible space and a valid underestimation function of the TPDF depending on the linear characteristics of the stability analysis problem were developed to guarantee the new branch and bound algorithm obtaining the epsilon-global convergence to the global solution of the TPDF. In comparison with the algorithms presented by Sun and Seider (Fluid Phase Equilib. 1995, 103, 213) and McDonald and Floudas (AlChE J. 1995, 41, 1798), the novel branch and bound algorithm is slightly slower; however, it can provide complete reliability for solving the phase stability analysis problem. Liquid-liquid equilibrium compositions were then calculated by the Newton-Raphson method (Fluid Phase Equilib. 1982, 9, 21) on the basis of the global minimum of TPDF. The preliminary calculation results for three ternary systems showed that the novel branch and bound algorithm can solve the global stability problem effectively.