The area method (AM) that minimizes the Gibbs energy by integrating, instead of differentiating, the Gibbs energy curve provides a sufficient condition for global Gibbs energy minimization rather than only a necessary condition provided by the flash equilibrium calculation method. However, it uses the method of exhaustion to search the positive maximum area, therefore requires a long calculation time. Here this method is modified as LSAM (local search area method), which is a repeated search shrinking vicinities of the liquid and gas equilibrium composition points located by previous rough search. The calculation time decreases to one over several thousands of AM’s or less. The experimental equilibrium data of benzene and propylene are used to demonstrate the merit of this method.