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

to be an orthogonal decomposition of the complete digraph $\dD_n$ by

$\dG$, if every arc of $\dD_n$ belongs to exactly two members of

$\mathcal{G}$ and the union of any two different elements from $\mathcal{G}$

contains precisely one pair of reverse arcs.

Given a digraph $\dH$, an $\dH$-family $m\dH$ is the vertex-disjoint union

of $m$ copies of $\dH$. In this paper, we consider orthogonal decompositions

by $\dH$-families. Our objective is to prove the existence of such an

orthogonal decomposition whenever certain necessary conditions hold and $m$

is sufficiently large.