  We are interested in those bundles $C$ on $\mathbb{P}^N$ which admit a
resolution of the form $$ 0 \to \mathbb{C}^s \otimes E \xrightarrow{\mu}
\mathbb{C}^t \otimes F \to C \to 0.$$ In this paper we prove that, under
suitable conditions on $(E,F)$, a generic bundle with this form is either
simple or canonically decomposable. As applications we provide an easy
criterion for the stability of such bundles on $\mathbb{P}^2$ and we prove the
stability when $E = \mathcal{O}$, $F = \mathcal{O}(1)$ and $C$ is an
exceptional bundle on $\mathbb{P}^N$ for $N \geq 2$.
