  Let ${\cal M}_{I\!\! P^3}(c_1,c_2)$ be the moduli space of stable rank-$2$
vector bundles on $I\!\! P^3$ with Chern classes $c_1$, $ c_2$. We prove the
following results.
  1) Let $0 \le \beta < \gamma $ be two integers, ($\gamma \ge 2)$, such that
$2\gamma-3\beta>0$; then ${\cal M}_{I\!\! P^3}(0,2\gamma^2-3\beta^2)$ is
singular (the case $\beta =0$ was previously proved by M. Maggesi).
  2) Let $0 \le \beta < \gamma $ be two odd integers ($\gamma \ge 5)$, such
that $2\gamma-3\beta+1>0$; then ${\cal M}_{I\!\!
P^3}(-1,2(\gamma/2)^2-3(\beta/2)^2+1/4)$ is singular.
  In particular ${\cal M}_{I\!\! P^3}(0,5)$, ${\cal M}_{I\!\! P^3}(-1,6)$ are
singular.
