  We extend a result by Fulton-Harris-Lazarsfeld in Brill-Noehter theory of
line bundles and, as well, a result by Aprod-Sernesi in theory of Secant Loci,
to the Brill-Noehter locus of stable bundles inside the moduli space of higher
rank stable vector bundles on a smooth projective algebraic curve. We give some
consequences of this extended result.
