Two cases are investigated. In the first case the electron distribution is assumed to have a loss‐cone feature. It is found that the plasma can amplify electromagnetic waves near the electron cyclotron frequency, as expected. However, the growth rate is significantly larger than that used in an approximate calculation in which a slightly different physical model was considered. The present discussion is restricted to the fast extraordinary‐ mode radiation. One of the important conclusions is that, due to the combined relativistic and loss‐cone effects, the cutoff frequency can be lower than the electron cyclotron frequency, a result in contrast with that obtained with the usual ’’cold plasma’’ approximation. In the second case a drift motion along the ambient magnetic field is studied. It is found that the cyclotron damping can occur under certain conditions.