Open trails in digraphs

It has been shown in [S. Cichacz, A. G rlich, Decomposition of complete bipartite graphs into open trails, Preprint MD 022, (2006)] that any bipartite graph $K_{a,b}$, is decomposable into open trails of prescribed even lengths. In this article we consider the corresponding question for directed graphs. We show that the complete directed graphs $\overleftrightarrow{K_n}$ and $\overleftrightarrow{K_{a,b}}$ are arbitrarily decomposable into directed open trails.