Assume that $k$ is algebraically closed. Let $\mathcal{X}$ be an SNC $S$-variety and denote by $(E_{i})_{i\in I}$ the set of irreducible components of $\mathcal{X}_{0}$. Let also $\mathcal{L}\in\Pic(\mathcal{X})$ and $m\in\mathbf{N}^{*}$. Then there exists an SNC $S$-scheme $\mathcal{X}^{\prime}$ and a finite surjective morphism $\rho:\mathcal{X}^{\prime}\to\mathcal{X}$ such that $\rho^{*}\mathcal{L}$ is divisible by $m$ in $\Pic(\mathcal{X}^{\prime})$ and $\rho^{*}E_{i}$ is smooth over $k$ (but possibly disconnected) for all $i\in I$.