Let $X$ a reduced analytic space, $n: W \rightarrow X$ the normalisation map, $W$ the normalisation of $X$ and $S$ the singular set of $X$. When we restrict $n$ to $W\setminus n^{-1}(S)$, we know that $n$ is a biholomorphism onto $X\setminus S$.
Is true that $n$ restricted to $W\setminus n^{-1}(S)$ is a homeomorphism bi-Lipschitz onto $X\setminus S$?