  Let $F$ be the function field of a curve over a non-archimedean local field.
Let $m \geq 2$ be an integer coprime to the characteristic of the residue field
of the local field. In this article, we show that every element in $H^{3}(F,
\mu_{m}^{\otimes 2})$ is of the form $\chi \cup (f) \cup (g)$, where $\chi$ is
in $H^{1}(F, \mathbb{Z}/m\mathbb{Z})$ and $(f)$, $(g)$ in $H^{1}(F, \mu_{m})$.
This extends a result of Parimala and Suresh, where they show this when $m$ is
prime and when $F$ contains $\mu_{m}$.
