  In this paper, we investigate the existence of self-dual MRD codes $C\subset
L^n$, where $L/F$ is an arbitrary field extension of degree $m\geq n$. We then
apply our results to the case of finite fields, and prove that if $m=n$ and
$F=\mathbb{F}_q$, a self-dual MRD code exists if and only if $q\equiv n\equiv 3
\ [4].$
