**MSC:**- 05C70 Factorization, matching, covering and packing
- 05B30 Other designs, configurations, See also {51E30}

collection of $n$ spanning subgraphs

$\vec{G}_1$, $\vec{G}_2$, ..., $\vec{G}_n$

of $\vec{K}_n$ such that \\

{\bf -} every directed edge of $\vec{K}_n$ belongs to exactly 1 of

the $\vec{G}_i$'s and \\

{\bf -} for every two digraphs $\vec{G}_i$ and $\vec{G}_j$ $(i \neq j)$

there is a unique two-element set $\{a, b\}$ of vertices such that

$\vec{G}_i$ contains the directed edge $(a, b)$ and $\vec{G}_j$

contains the directed edge $(b, a)$. \\

It is proven that there exists an orthogonal cover of $\vec{K}_n$,

where the $\vec{G}_i$'s consist of short directed cycles, for

all $n \geq 4, $ with a few possible exceptions. We conclude by

establishing the existence of an orthogonal cover of $\vec{K}_n$,

where the $\vec{G}_i$'s have maximum outdegree and maximum indegree

one, for all $n \geq 2$. This gives another proof of the directed version of a

problem of Chung and West.