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Let $k$ be a field and let $H$ denote a pointed Hopf $k$-algebra withantipode $S$. We are interested in determining the order of $S$. Building onthe work done by Taft and Wilson $[7]$, we define an invariant for $H$, denoted$m_{H}$, and prove that the value of this invariant is connected to the orderof $S$. In the case where $\operatorname{char}k=0$, it is shown that if $S$ hasfinite order then it is either the identity or has order $2m_{H}$. If inaddition $H$ is assumed to be coradically graded, it is shown that the order of$S$ is finite if and only if $m_{H}$ is finite. We also consider the case where$\operatorname{char}k=p>0$, generalising the results of $[7]$ to theinfinite-dimensional setting.

A note on the order of the antipode of a pointed Hopf algebra