  Using properties of skew-Hamiltonian matrices and classic connectedness
results, we prove that the moduli space $M_{ort}^0(r,n)$ of stable rank $r$
orthogonal vector bundles on $\mathbb{P}^2$, with Chern classes
$(c_1,c_2)=(0,n)$, and trivial splitting on the general line, is smooth
irreducible of dimension $(r-2)n-{r \choose 2}$ for specific values of $r$ and
$n$.
