A volume, denoted unstable eigenvolume, located very close to the pinch points occuring one in each minimum refluxed rectification column section, and spanned by the eigenvectors corresponding to eigenvalues greater than one of the functional matrix of rigorous plate-to-plate calculation contains the initial points of all potentially feasible rigorous separation paths leaving the pinch into the feed component space. Searching the unstable eigenvolumes for the initial points of two intersecting separation paths constitutes a new rigorous minimum reflux method. The intersection of merely the unstable eigenspaces is a new algebraic approximate criterion for minimum reflux.