The filamentation of a femtosecond laser pulse with a non-Gaussian transverse intensity profile has been studied experimentally and by numerical simulation. The results demonstrate that the distance to the filamentation region can be evaluated using the Marburger formula in which the critical power of self-focusing at a beam quality factor M2 exceeds that for a Gaussian beam by a factor of (M2)2. The characteristics of the filament resulting from self-focusing depend little on the beam quality factor: both the filament energy and diameter coincide. If the beam is passed through an aperture, a filament forms on a diffraction ring, and its parameters coincide with those of a filament formed with no slit (provided the initial pulse parameters coincide).