A method is presented that allows the calculation of phase diagrams (spinodal, binodal, and tie lines) of quaternary mixtures on the basis of the Gibbs energy of mixing Delta G. No derivatives of Delta G with respect to the composition variables are required. This method is particularly useful in cases where the composition dependence of Delta G is very complex, and no analytical representation of Delta G can be found. Phase diagrams have been calculated on the basis of the Flory-Huggins theory for mixtures of four polymers. Blends that phase separate because of very favorable interactions (negative interaction parameters) were of particular interest. In this case miscibility gaps can be located inside the tetrahedron composed of the Gibbs phase triangles of the four completely miscible ternary subsystems. For symmetrical mixtures of K components (identical chain lengths and interaction parameters) equations are presented that allow the calculation of K-phase and (K - 1)-phase regions for any value of K.