  For any even integer $k\ge 6$, integer $d$ such that $k/2\le d\le k-1$, and
sufficiently large $n\in (k/2)\mathbb N$, we find a tight minimum $d$-degree
condition that guarantees the existence of a Hamilton $(k/2)$-cycle in every
$k$-uniform hypergraph on $n$ vertices. When $n\in k\mathbb N$, the degree
condition coincides with the one for the existence of perfect matchings
provided by R\"odl, Ruci\'nski and Szemer\'edi (for $d=k-1$) and Treglown and
Zhao (for $d\ge k/2$), and thus our result strengthens theirs in this case.
