Characterization of the Lovelock gravity by Bianchi derivative

We prove the theorem: The second-order quasilinear differential operator as a second-rank divergence-free tensor in the equation of motion for gravitation could always be derived from the trace of the Bianchi derivative of the fourth-rank tensor, which is a homogeneous polynomial in curvatures. The existence of such a tensor for each term in the polynomial Lagrangian is a new characterization of the Lovelock gravity.