In this communication, we report for the first time the possible existence of a point of inflection in the profile of a local reactivity descriptor around the transition state. The saddle point of the given reaction coincides with this inflection point which becomes transparent when two such profiles corresponding to bond making and bond breaking processes respectively intersect at the transition state for the thermoneutral reactions. The corresponding ramification of the Hammond postulate for the exo(endo) thermic reactions is also discussed.