For a smooth algebraic curve C of genus g

4, let

(r, d) be the moduli space of semistable bundles of rank r

2 over C with fixed determinant of degree d. When (r,d) = 1, it is known that

(r, d) is a smooth Fano variety of Picard number 1, whose rational curves passing through a general point have degree

r with respect to the ampl generator of Pic(

(r, d)). In this paper, we study the locus swept out by the rational curves on

(r, d) of degree < r. As a by-product, we present another proof of Torelli theorem on

(r, d).