  Let $\cM_r$ denote the moduli space of semi-stable rank-$r$ vector bundles
with trivial determinant over a smooth projective curve $C$ of genus $g$. In
this paper we study the base locus $\cB_r \subset \cM_r$ of the linear system
of the determinant line bundle $\cL$ over $\cM_r$, i.e., the set of semi-stable
rank-$r$ vector bundles without theta divisor. We construct base points in
$\cB_{g+2}$ over any curve $C$, and base points in $\cB_4$ over any
hyperelliptic curve.
