A new approach to the problem of the radiation emitted from a localized external current source embedded in a magnetoplasma is described. It is argued that the calculation of the fields in the radiation zone can be substantially simplified by adopting at the outset a suitable parametrization of the dispersion surface. We illustrate the approach by calculating the far fields using the full expression for the dielectric tensor of a warm magnetized electron gas. In this case one can take the angle of rotation about the external magnetic field and the square of the refractive index as the curvilinear co-ordinates of the dispersion surface. The form of the surfaces of constant phase and the amplitudes of the emitted waves are described for each topologically different region of parameter space and their structures are related to the shapes of the refractive index surfaces. Attention is also drawn to the existence of locally cylindrical waves that can produce beams which are highly collimated in the direction of the external magnetic field.