Given natural numbers m and p with m ≥ p + 2 ≥ 3, allM fm-natural operators A sending closed (p + 2)-forms H on m-manifolds M into R-bilinear operators AH transforming pairs of couples of vector fields and p-forms on M into couples of vector fields and p-forms on M are found. If m ≥ p + 2 ≥ 3, all M fm-natural operators A (as above) such that AH satisfies the Jacobi identity in Leibniz form are extracted, and that the twisted Courant bracket [−,−]H is the uniqueM fm-natural operator AH (as above) satisfying the Jacobi identity in Leibniz form and some normalization condition is deduced.