In some applications, due to regularity restriction, 2nd-order elliptic problems have no divergent forms, and therefore we need to discretize the 2nd-order derivatives directly. In this work, we construct a new Petrov-Galerkin method by using C1-conforming finite element for the trial space and L2-discontinuous element for the test space. We prove that the numerical solution by the new method converges to the exact solution with $2k-1$-rate ($k$ is the polynomial degree) at the nodal points for both function value and gradient under rectangular meshes.