A new nonlinear electromagnetic mode in a magnetized plasma is predicted. Its existence depends on the interaction of an intense, circularly polarized electromagnetic wave with a plasma, where quantum electrodynamical photon–photon scattering is taken into account. This scattering gives rise to a new coupling between the matter and the radiation. Specifically, we consider an electron–positron plasma and show that the propagation of the new mode is admitted. It could be of significance in pulsar magnetospheres, and result in energy transport between the pulsar poles.