This paper presents an investigation of the self-focusing of an elliptically gaussian laser beam propagating along the static magnetic field in a non-linearly absorbing magnetoplasma. The electron concentration and temperature and the static magnetic field are allowed to be non-uniform. The direct coupling as well as the indirect coupling between the right- and left-handedly polarized modes has been taken into account. Coupled equations for the beamwidth parameters have been derived by using the Akhmanov approach. It is seen that axial symmetry of the intensity distributions of the two modes is not preserved in the presence of the direct coupling. The variations of the beamwidth parameters become considerably aperiodic on account of the indirect coupling and non-uniformity in the plasma parameters. Though the investigation is explicitly related to a magnetoplasma, the analysis presented herein can be easily extended for some other anisotropic media.