Let $\mathscr{V}$ be a lattice of $V$. We assume that, as an $\mathfrak{o}_{k}$-module, $\mathscr{V}$ admits a free basis $(e_{1},\ldots,e_{r})$. Then $(e_{1},\ldots,e_{r})$ is an orthonormal basis of $V$ with respect to $\|\raisebox{1.72218pt}{.}\|_{\mathscr{V}}$.