A numerical method has been proposed for solving strongly nonlinear equations by improving the Wegstein method. The feature of the proposed method (modified Wegstein method, MWS) is to eliminate one of the direct iteration steps in the iterative calculation procedure of the Wegstein method with the purpose of reducing the C.P.U. time required. Applying MWS, an algorithm is proposed for calculating the dew point of a non-ideal system by means of simulataneous correcting of temperature and component activity coefficient. The superiority of the proposed method is shown by sample calculations of bubble and dew points for several examples.