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We use results of M. Aprodu and E. Sernesi to extend a result byFulton--Harris--Lazarsfeld in Brill--Noether theory of line bundles %and, aswell, a result by Aprod-Sernesi in theory of Secant Loci,  to Brill--Noether loci of stable bundles inside the moduli space of rank twostable vector bundles on a smooth projective algebraic curve. As a consequence;if $B^k_{2, d}$ is of expected dimension, then we prove that its smoothness isequivalent with the smoothness of $B^{k}_{2, d+1}$.

Excess dimensions of Brill--Noether schemes of rank two stable bundles