Adopting high-order global cover function can enhance the calculation precision of the numerical manifold method, but the high-order function in common use related to global coordinate may cause ill-condition of stiffness matrix in the numerical manifold method and affect the computational precision of the small boundary blocks that occupy a part of mathematical meshes. Based on the local cover function proposed by orther researchers, an improved local cover function is presented, resulting in effective improvement of the quality of stiffness matrix and the stress precision of small blocks on model boundary. A relationship between the improved local cover function and the global cover function is also established and this improved function can simplify the derivation of formulation.