  We perform the renormalization group analysis on the dynamical symmetry
breaking under strong external magnetic field, studied recently by Gusynin,
Miransky and Shovkovy. We find that any attractive four-Fermi interaction
becomes strong in the low energy, thus leading to dynamical symmetry breaking.
When the four-Fermi interaction is absent, the $\beta$-function for the
electromagnetic coupling vanishes in the leading order in $1/N$. By solving the
Schwinger-Dyson equation for the fermion propagator, we show that in $1/N$
expansion, for any electromagnetic coupling, dynamical symmetry breaking occurs
due to the presence of Landau energy gap by the external magnetic field.
