  We study the commutant of the vertex operator algebra
$\mathcal{L}_{\widehat{\mathfrak{sl}}_2}(4,0)$ in the cyclic permutation
orbifold model $(\mathcal{L}_{\widehat{\mathfrak{sl}}_2}(1,0)^{\otimes
4})^\tau$ with $\tau=(1\,2\,3\,4)$. It is shown that the commutant is
isomorphic to a ${\mathbb Z}_2\times{\mathbb Z}_2$-orbifold model of a tensor
product of two lattice type vertex operator algebras of rank one.
