  We give a criterion for a set of $n$ hyperbolic isometries of a
$\mathrm{CAT}(0)$ metric space $X$ to generate a free group on $n$ generators.
This extends a result by Alperin, Farb and Noskov who proved this for 2
generators under the additional assumption that $X$ is complete and has no fake
zero angles. Moreover, when $X$ is locally compact, the group we obtain is also
discrete.
