  Let $n, s$ be positive integers such that $n$ is sufficiently large and $s\le
n/3$. Suppose $H$ is a 3-uniform hypergraph of order $n$. If $H$ contains no
isolated vertex and $deg(u)+ deg(v) > 2(s-1)(n-1)$ for any two vertices $u$ and
$v$ that are contained in some edge of $H$, then $H$ contains a matching of
size $s$. This degree sum condition is best possible and confirms a conjecture
of the authors [Electron. J. Combin. 25 (3), 2018], who proved the case when
$s= n/3$.
