Let
F
F
be the function field of a curve over a non-archimedean local field. Let
m
≥
2
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
,
μ
m
⊗
2
)
H^{3}(F, \mu _{m}^{\otimes 2})
is of the form
χ
∪
(
f
)
∪
(
g
)
\chi \cup (f) \cup (g)
, where
χ
\chi
is in
H
1
(
F
,
Z
/
m
Z
)
H^{1}(F, \mathbb {Z}/m\mathbb {Z})
and
(
f
)
(f)
,
(
g
)
(g)
in
H
1
(
F
,
μ
m
)
H^{1}(F, \mu _{m})
. This extends a result of Parimala and Suresh [Ann. of Math. (2) 172 (2010), pp. 1391–1405], where they show this when
m
m
is prime and when
F
F
contains
μ
m
\mu _{m}
.