  A non-Abelian Born-Infeld theory is presented. The square root structure that
characterizes the Dirac-Born-Infeld (DBI) action does not appear. The procedure
is based on an Abelian theory proposed by Erwin Schr\"{o}dinger that, as he
showed, is equivalent to Born-Infeld theory. We briefly mention other possible
similar proposals. Our results could be of interest in connection with string
theory and possible extensions of well known physical results in the usual
Born-Infeld Abelian case.
