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 lefthandedly 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 .