The Natural Operators Lifting 1-Forms to r-Jet Prolongation of the Tangent Bundle

We prove that for n-manifolds (n 3) the set of all natural operators T^* T^*(J^rT) is a free [2(r + 1)² + 1]-dimensional module over C (R^r+1). We construct explicitly the basis of the C (R^r+1)-module.