# Henselization of valued field

Let $(k, \nu)$ be a valued field $(k_{1}, \nu_{1})$ is a Hensilization of $(k, \nu)$. Is there exist a another valuation $\nu^{'}$ on $k$ different from $\nu$ such that $(k_{1}, \nu_{2})$ is a Hensilization extension of $(k, \nu^{'})$. Thanks

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If I understand "henselization" correctly, $\nu$ and $\nu'$ must both equal the restriction of $\nu_1$ to $k$. –  Laurent Moret-Bailly Jan 26 at 9:43