  A new nonlinear electromagnetic wave 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.
