Let ${mathcal I}(n)$ denote the moduli space of rank $2$ instanton bundles of charge $n$ on ${mathbb P}^3$. We know from several authors that ${mathcal I}(n)$ is an irreducible, nonsingular and affine variety of dimension $8n-3$. Since every rank $2$
instanton bundle on ${mathbb P}^3$ is stable, we may regard ${mathcal I}(n)$ as an open subset of the projective Gieseker--Maruyama moduli scheme ${mathcal M}(n)$ of rank $2$ semistable torsion free sheaves $F$ on ${mathbb P}^3$ with Chern classes $c_1=c_3=0$ and $c_2=n$, and consider the closure $overline{{mathcal I}(n)}$ of ${mathcal I}(n)$ in ${mathcal M}(n)$. We construct some of the irreducible components of dimension $8n-4$ of the boundary $partial{mathcal I}(n):=overline{{mathcal I}(n)}setminus{mathcal I}(n)$. These components generically lie in the smooth locus of ${mathcal M}(n)$ and consist of rank $2$ torsion free instanton sheaves with singularities along rational curves.
