  A $2k$-matching is a perfect matching of the complete graph on $2k$ vertices.
Two $2k$-matchings are defined to be $t$-intersecting if they have at least $t$
edges in common. The main result in this paper is that if $k \geq 3t/2+1$, then
the largest system of $t$-intersecting $2k$-matchings has size $(2(k-t)-1)!! =
\prod_{i=0}^{k-t-1}(2k-2t-2i-1)$ and the only systems that meet this bound
consist of all $2k$-matchings that contain a set of $t$ disjoint edges.
Further, this bound on $k$ is sharp for $t\geq 6$. The method used is this
paper is similar to the proof of the complete Erd\H{o}s-Ko-Rado theorem given
by Ahlswede and Khachatrian.
