  It was shown recently that an $n$-extension closed subcategory $\mathscr A$
of a Krull-Schmidt $(n+2)$-angulated category has a natural structure of an
$n$-exangulated category. In this article, we prove that its idempotent
completion $\widetilde{\mathscr A}$ admits an $n$-exangulated structure. It is
not only a generalization of the main result of Lin, but also gives an
$n$-exangulated category which is neither $n$-exact nor $(n+2)$-angulated in
general.
