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Isochronal and isothermal annealing treatments were carried out on GaAsN films grown by chemical beam epitaxy to clarify the evolution of a nonradiative recombination center, at an average energy level of 0.33 eV below the conduction band minimum of the alloy. This lattice defect showed a strong persistence during post-thermal annealing even under critical annealing conditions. By considering as-grown samples as references and after optimizing the temperature and time of annealing, the trapping density of this recombination center could be reduced to one-half. Since the origin of this N-related recombination center was tentatively considered as the split interstitial (N–As) As, we suggest that the evolution of its density could be explained in great part to the diffusion behavior of As atoms during thermal stress.