Recent development of the high-order, low-order (HOLO) method has shown promising results for solving thermal radiative transfer problems. The HOLO algorithm is a moment-based acceleration, similar to the well-known nonlinear diffusion acceleration and coarse-mesh finite difference methods. In this work, we introduce a new spatial-differencing scheme for the low-order (LO) system based on the corner-balance method and analyze an asymptotic diffusion property for a one-dimensional gray equation. An asymptotic analysis indicates that the new spatial-differencing scheme possesses the equilibrium diffusion limit. Numerical examples demonstrate significant improvements in the solution accuracy compared to the LO finite-volume discretization with a discontinuous source reconstruction.