Let $V$ be a paracompact strictly $K$-analytic space with a line bundle $L$. If $\|\ \|$ is a continuous metric on $L$, then there is a sequence $(\|\ \|_{n})_{n\in{\mathbb{N}}}$ of piecewise ${\mathbb{Q}}$-linear metrics on $L$ which converges uniformly to $\|\ \|$.