  In this note we study the moduli space of rank two semistable sheaves on a
smooth cubic hypersurface $X\subset\mathbb{P}^{4}$ with $c_{1}=0$, $c_{2}=2$
and $c_{3}=0$. We show that it is isomorphic to the blow-up of the intermediate
jacobian $J(X)$ of $X$ along the Fano surface of $X$. We complete previous
results of Iliev-Markushevich AG/9910058 and Markushevich-Tikhomirov
AG/9910063.
