When a reacting system has some elements of point-symmetry,according to Noethor's theorem,we can find a corresponding invariable-pointy.It follows at once that the selection roles for the relative relation may be established.There is a new symmetry other than the point-symmetry for the sigmatropic reaction.According to this symmetry,if we carry ont a reaction-reversal operation and some point-symmetry operation fragment consecutively,the final state of the system or fragments is indistinguishable from the initial state.