  In this paper, we characterize $C^2$-smooth totally geodesic isometric
embeddings $f\colon \Omega\to\Omega'$ between bounded symmetric domains
$\Omega$ and $\Omega'$ which extend $C^1$-smoothly over some open subset in the
Shilov boundaries and have nontrivial normal derivatives on it. In particular,
if $\Omega$ is irreducible, there exist totally geodesic bounded symmetric
subdomains $\Omega_1$ and $\Omega_2$ of $\Omega'$ such that $f = (f_1, f_2)$
maps into $\Omega_1\times \Omega_2\subset \Omega$ where $f_1$ is holomorphic
and $f_2$ is anti-holomorphic totally geodesic isometric embeddings. If
$\text{rank}(\Omega')<2\text{rank}(\Omega)$, then either $f$ or $\bar f$ is a
standard holomorphic embedding.
