  An Euler tour in a hypergraph (also called a rank-2 universal cycle or
1-overlap cycle in the context of designs) is a closed walk that traverses
every edge exactly once. In this paper, we define a covering $k$-hypergraph to
be a non-empty $k$-uniform hypergraph in which every $(k-1)$-subset of vertices
appear together in at least one edge. We then show that every covering
$k$-hypergraph, for $k\geq 3$, admits an Euler tour if and only if it has at
least two edges.
