Let $V\subset{{\bf R}}^{n}$ be a connected open set, $\varphi\in{\cal O}^{\times}_{{({\bf G}_{m}^{an})}^{n}}(\pi_{can}^{-1}(V))$ be an invertible analytic function. Then the function $val_{x}(\varphi(x))$ is constant along fibers of $\pi_{can}$, and it is a pull-back of a ${\bf Z}$-affine function on ${{\bf R}}^{n}$.