Let $\Omega \subset \mathbb C^n$ be a domain with $C^2$ boundary. The following conditions are equivalent: the Levi form of a defining function is non-negative on $H(\partial\Omega)$; every boundary point has a neighbourhood $U$ such that $\Omega\cap U$ admits a plurisubharmonic exhaustion; and $\Omega$ is locally pseudoconvex at the boundary in the sense used in SCV I. If, in addition, these local data are combined with an exhaustion of the interior, this agrees with the usual global pseudoconvexity of $\Omega$.