  For a smooth projective curve C with genus g >= 2 and a degree 1 line bundle
L on C, let M := SU_{C}(r;L) be the moduli space of stable vector bundles of
rank r and with the fixed determinant L. In this paper, we study the small
rational curves on M and estimate the codimension of the locus of the small
rational curves. In particular, we determine all small rational curves when r =
3.
