  We discuss the polarization selection rules for splitting of the two
principal electromagnetic modes that propagate in a vacuum polarized by a
superstrong magnetic field (B>0.1B_{cr} ~ 4x10^{12} G). We show that below the
threshold of free pair creation the selection rules found by Adler in the limit
of weak dispersion remain unaffected by taking the resonant effects into
consideration, i.e., splitting of one mode is strictly forbidden, while
splitting of the other is allowed.
