Using the self-convergent beam width method, the beam width propagation and beam-propagation parameters of hard-edge diffracted super-Gaussian beams are studied. It is found that the self-convergent beam width of super-Gaussian beams obeys the same law as that of the beam width based on the second-order moments without truncation, when the self-convergent-width factor satisfies a certain condition. Therefore, the beam propagation factor (M2-factor) obtained by using this method is invariable upon propagation. Meanwhile, a detailed comparison between the self-convergent beam width method and the asymptotic approach is made and the equivalence between the two methods is discussed. In addition, a concise physical meaning of the self-convergent beam width method is given.