  Let $\mathcal{C}$ be a $k$-linear category with split idempotents, and
$\Sigma:\mathcal{C}\rightarrow\mathcal{C}$ an automorphism. We show that there
is an $n$-angulated structure on $(\mathcal{C},\Sigma)$ under certain
conditions. As an application, we obtain a class of examples of $n$-angulated
categories from self-injective algebras.
