  Let $f_s: X_s \to {\bf {P}}^2$ be the blowing-up of $s$ distinct points and
$E$ a vector bundle on $X_s$. Here we give a cohomological criterio which is
equivalent to $E \cong f_s^\ast (A)$ with $A$ a direct sum of line bundles. We
also some cohomological characterizations of very particular rank 2 vector
bundles on ${\bf {P}}^2$.
