In this paper, a new spatial homogenization method in transport theory is developed that reproduces the heterogeneous solution by using conventional flux-weighted homogenized cross sections. By introducing an additional source term via an auxiliary cross section, the resulting homogeneous transport equation becomes consistent with the heterogeneous equation, enabling easy implementation into existing solution methods/codes. This new method utilizes on-the-fly rehomogenization, performed at the assembly level, to correct for the effect of core environment on the homogenized cross sections. The method is derived in general geometry and continuous energy and implemented and tested in fine-group one-dimensional slab geometries typical of boiling water reactor and gas-cooled reactor cores. The test problems include two single-assembly and four-core configurations.