This method, which takes into account the influence of assembly heterogeneity on neutron leakage, is based on the heterogeneous B1 formalism, which assumes the existence of a fundamental mode in an infinite and regular lattice of heterogeneous assemblies. A simplified formalism, TIBERE, is presented that allows one to define directional space-dependent leakage coefficients. This method, introduced for two-dimensional x-y geometry in the APOLLO-2 multigroup transport code, uses classical and directional first-flight collision probabilities. One can now define leakage cross sections as additional absorption cross sections that have space and energy dependence, as well as all other cross sections. Hence, one obtains perfectly consistent reaction and leakage rates used in an equivalence procedure, determining cell-homogenized parameters for a whole core calculation. The study of this refined heterogeneous leakage treatment was undertaken because of the insufficiency of the homogeneous leakage model, especially in cases when an assembly contains voided zones or almost voided zones, i.e., zones with a long mean free path, so that the streaming effect may become important. The fission rate comparisons between the EPICURE reactor experimental results and the results of the corresponding whole reactor calculations were accomplished, with leakages calculated by the homogeneous and the TIBERE procedures of the APOLLO-2 code.