Abstract: This paper aims at developing a rigorous method for determining minimum reflux ratio in the distillation of "tangent systems" which are defined as those with concave VLE curves. Two pinch zones in the rectifying or stripping section may be obtained with previously published models when different initial values are chosen. This behavior naturally leads to the fact that the calculated minimum reflux ratio could be lower than the "real "one. On the basis of Chiens method, the authors used parabolic interpolation to acquire the maximum condensor in the two pinch zones and then find out the "real" minimum reflux ratio. The results were verified and showed adequate precision. The algorithm presented in this paper can be used not only for tangent systems, but also for conventional distillation systems.