Among the methods with cell-centered unknowns on large distortion meshes,most adopt the vertex unknowns indirectly to discretize diffusion equations such that their accuracy is ultimately determined by he approximation to the vertex unknowns.In this paper,taking advantage of the high-order accuracy of the "twin-fitting" method especially on discontinuous diffusion coefficients,a new treatment for the vertex unknowns is developed to apply to a nine-point scheme.