A new method has been developed to solve the problem of complete integration of the Gibbs-Duhem equation along phase boundaries in a c-component and c-1-phase system. Two variables, (△_1)_(1i)=D_i/D_i and (△_i)_(1i)=D_i/D_(1i), are introduced into the Gibbs-Duhem equation for multicomponent systems. And the function φ suggested by Chou for use in a miscibility gap of ternary systems is extended. Activities of component f on whole phase boundaries may be calculated from the known experimental values of a_1 by means of the modified Gibbs-Duhem equation without integral difficulties.