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We discuss the equivalence between a string theory and the two-dimensionalYang-Mills theory with SU(N) gauge group for finite N. We find a sector whichcan be interpreted as a sum of covering maps from closed string world-sheets tothe target space, whose covering number is less than N. This gives anasymptotic expansion of 1/N whose large N limit becomes the chiral sectordefined by D.Gross and W.Taylor. We also discuss that the residual part of thepartition function provides the non-perturbative corrections to theperturbative expansion.Comment: 15 pages, no figures, LaTeX2e, typos corrected, final version to  appear in Modern Physics Letters

STRING THEORETICAL INTERPRETATION FOR FINITE N YANG–MILLS THEORY IN TWO DIMENSIONS