Let λ be a dominant weight and let Φ(λ) be the saturated weight set with highest weight λ.The weight polytope Pλ is defined as the convex hull of Φ(λ).This paper provides an elementary proof that there is a natural bijection between the set of orbits of weight polytope under action of Weyl group and set of parabolic subgroups of Weyl group.The bijection, now called Putcha-Renner recipe, is found by Putcha and Renner in linear algebraic monoid theory.