  Let $X\subseteq{\mathbb P}^{n+1}$ be an integral hypersurface of degree $d$.
We show that each locally Cohen-Macaulay instanton sheaf $\mathcal E$ on $X$
with respect to $\mathcal O_X\otimes\mathcal O_{\mathbb P^{n+1}}(1)$ in the
sense of Definition 1.3 in arXiv:2205.04767 [math.AG] yields the existence of
Steiner bundles $\mathcal G$ and $\mathcal F$ on $\mathbb P^{n+1}$ of the same
rank $r$ and a morphism $\varphi\colon \mathcal G(-1)\to\mathcal F^\vee$ such
that the form defining $X$ to the power $\mathrm{rk}(\mathcal E)$ is exactly
$\det(\varphi)$. We inspect several examples for low values of $d$, $n$ and
$\mathrm{rk}(\mathcal E)$. In particular, we show that the form defining a
smooth integral surface in $\mathbb P^3$ is the pfaffian of some skew-symmetric
morphism $\varphi\colon \mathcal F(-1)\to\mathcal F^\vee$, where $\mathcal F$
is a suitable Steiner bundle on $\mathbb P^3$ of sufficiently large even rank.
