Let $(V,\lVert\mathord{\cdot}\rVert_{V})$ be a finite-dimensional ultrametrically normed vector space over $k$. Suppose that $(k,|\cdot|)$ is discretely valued. If $\{e_{i}\}_{i\in\{1,\dots,n\}}$ is a basis of $V$ such that $\{\log\lVert e_{i}\rVert\}_{i\in\{1,\dots,n\}}$ are $\mathbb{Q}$-independent in $\mathbb{R}/H(k,\lvert\mathord{\cdot}\rvert)$, then $\{e_{i}\}_{i\in\{1,\dots,n\}}$ is an orthogonal basis.