  We discuss the equivalence between a string theory and the two-dimensional
Yang-Mills theory with SU(N) gauge group for finite N. We find a sector which
can be interpreted as a sum of covering maps from closed string world-sheets to
the target space, whose covering number is less than N. This gives an
asymptotic expansion of 1/N whose large N limit becomes the chiral sector
defined by D.Gross and W.Taylor. We also discuss that the residual part of the
partition function provides the non-perturbative corrections to the
perturbative expansion.
