Let $L$ be a real $m$-dimensional submanifold of $\mathbin{\mathbb{C}}^{m}$. Then $L$ admits an orientation making it into an SL submanifold of $\mathbin{\mathbb{C}}^{m}$ if and only if $\omega|_{L}\equiv 0$ and $\mathop{\rm Im}\Omega|_{L}\equiv 0$.