In ferromagnets and antiferromagnets, the coupling between phonons and magnons cannot be overlooked, because of the exchange interaction changing with the distance between the magnetic ions. In this article, the possible effect of this coupling on the infrared absorption in magnetic insulators has been considered. The transition involved consists of the excitation of an optical phonon by the interaction with radiation field and simultaneously that of two magnons and a phonon due to the perturbation of the phonon-magnon coupling. It produces an absorption band with frequencies higher than the edge of the lattice absorption. Since the total spin component Sz must be conserved, this effect should not be found in ferromagnetic insulators. If the Néel temperature of an antiferromagnet is high enough and the distribution of spin wave states vs. energy has a sharp maximum the predicted absorption band becomes observable. Our treatment is aimed at the 0.24 eV absorption band of NiO. Its peak energy and absorption constant are calculated. The results appear in fair agreement with the experimental findings. Finally, it is pointed out that the transition process adopted by Mizuno and Koide for explaining the same phenomenon can only offer a secondly effect in comparison with ours.