  A $k$-tournament $H$ on $n$ vertices is a pair $(V, A)$ for $2\leq k\leq n$,
where $V(H)$ is a set of vertices, and $A(H)$ is a set of all possible
$k$-tuples of vertices, such that for any $k$-subset $S$ of $V$, $A(H)$
contains exactly one of the $k!$ possible permutations of $S$. In this paper,
we investigate the relationship between a hyperdigraph and its corresponding
normal digraph. Particularly, drawing on a result from Gutin and Yeo, we
establish an intrinsic relationship between a strong $k$-tournament and a
strong tournament, which enables us to provide an alternative (more
straightforward and concise) proof for some previously known results and get
some new results.
