Let $\mathfrak{X}$ be a strongly nondegenerate strictly polystable formal scheme over $K^{\circ}$. Any formal open covering of $\mathfrak{X}$ admits a refinement $\{\mathfrak{U}^{\prime}\}$ by formal open subsets $\mathfrak{U}^{\prime}$ as in Definition 2.3 such that

1. i)

   Every $\mathfrak{U}^{\prime}$ is a formal affine open subscheme of $\mathfrak{X}$,

2. ii)

   there is a distinguished stratum $S$ of $\tilde{\mathfrak{X}}$ associated to $\mathfrak{U}^{\prime}$ such that for any stratum $T$ of $\tilde{\mathfrak{X}}$, we have $S\subseteq\overline{T}$ if and only if $\tilde{\mathfrak{U}^{\prime}}\cap\overline{T}\neq\emptyset$,

3. iii)

   $\tilde{\psi}^{-1}(\{\tilde{\boldsymbol{0}}\}\times\widetilde{\mathfrak{X}(m)})$ is the stratum of $\tilde{\mathfrak{U}^{\prime}}$ which is equal to $\tilde{\mathfrak{U}^{\prime}}\cap S$ for the distinguished stratum $S$ associated to $\mathfrak{U}^{\prime}$,

4. iv)

   every stratum of $\tilde{\mathfrak{X}}$ is the distinguished stratum of a suitable $\mathfrak{U}^{\prime}$.