In recent years there has been active interest in process simulation in the complex domain. In this work, a new procedure regarding fixed-point continuation method in complex domain using bifurcation theory has been proposed. Based on this method, homotopy branches in real space are connected to each other through bifurcation branches in complex space. Therefore, all of the solution branches are found by just one initial guess. There are some examples presented to show how it can be done in solving nonlinear sets of solutions, specially in phase equilibrium problems which contain the most nonlinearities in process simulations. The results are quit interesting and it can be extended to the flowsheet calculations.