  In this paper we consider the Brill-Noether locus $W_{\underline d}(C)$ of
line bundles of multidegree $\underline d$ of total degree $g-1$ having a
nonzero section on a nodal reducible curve $C$ of genus $g\geq2$. We give an
explicit description of the irreducible components of $W_{\underline d}(C)$ for
a semistable multidegre $\underline d$. As a consequence we show that, if two
semistable multidegrees of total degre $g-1$ on a curve with no rational
components differ by a twister, then the respective Brill-Noether loci have
isomorphic components.
