  For a compact 2-orbifold with negative Euler characteristic $\mathcal O^2$,
the variety of characters of $\pi_1(\mathcal O^2)$ in $\mathrm{SL}_{n}(\mathbb
R)$ is a non-singular manifold at $\mathbb C$-irreducible representations. In
this paper we prove that when a $\mathbb C$-irreducible representation of
$\pi_1(\mathcal O^2)$ in $\mathrm{SL}_{n}(\mathbb R)$ is viewed in
$\mathrm{SL}_{n+1}(\mathbb R)$, then the variety of characters is singular, and
we describe the singularity.
