  Let $E$ be a CM number field and $F$ its maximal real subfield. We prove a
level-raising result for regular algebraic conjugate self-dual automorphic
representations of $GL_n(\mathbb{A}_E)$. This generalizes previously known
results of Thorne by removing certain hypotheses occurring in that work. In
particular, the level-raising prime $p$ is allowed to be unramified as opposed
to inert in $F$, the field $E/F$ is not assumed to be everywhere unramified,
and the field $E$ is allowed to be a general CM field.
