  Let $X = (V,E)$ be a graph. A subset $C \subseteq V(X)$ is a \emph{perfect
code} of $X$ if $C$ is a coclique of $X$ with the property that any vertex in
$V(X)\setminus C$ is adjacent to exactly one vertex in $C$. Given a finite
group $G$ with identity element $e$ and $H\leq G$, $H$ is a \emph{subgroup
perfect code} of $G$ if there exists an inverse-closed subset $S \subseteq
G\setminus \{e\}$ such that $H$ is a perfect code of the Cayley graph
$\operatorname{Cay}(G,S)$ of $G$ with connection set $S$. In this short note,
we give an infinite family of finite groups $G$ admitting a non-normal subgroup
perfect code $H$ such that there exists $ g\in G$ with $g^2\in H$ but $(gh)^2
\neq e$, for all $h \in H$; thus, answering a question raised by Wang, Xia, and
Zhou in [Perfect sets in Cayley graphs. {\it arXiv preprint} arXiv:2006.05100,
2020].
