  We prove that the moduli space of stable sheaves of rank 2 with a certain
Chern classes on a smooth quadric $Q$ in $\PP_3$, is isomorphic to $\PP_3$.
Using this identification, we give a new proof that a certain Brill-Noether
locus on a non-hyperelliptic curve of genus 4, is isomorphic to the
Donagi-Izadi cubic threefold.
