  Although nonsymmorphic symmetry protects $\mathbb{Z}_4$ topology for
Hermitian systems, non-Hermitian topological phenomena induced by such a unique
topological structure remain elusive. In this paper, we elucidate that systems
with glide symmetry exhibit non-Hermitian skin effects (NHSE) characterized by
$\mathbb{Z}_4$ topology. Specifically, numerically analyzing a two-dimensional
toy model, we demonstrate that the $\mathbb{Z}_4$ topology induces the NHSE
when the topological invariant takes $\nu=1,2$. Furthermore, our numerical
analysis demonstrates that the NHSE is destroyed by perturbations preserving
the relevant symmetry when the $\mathbb{Z}_4$-invariant takes $\nu=4$.
