  Let $\vec{T}_k$ be the transitive tournament on $k$ vertices. We show that
every oriented graph on $n=4m$ vertices with minimum total degree
$(11/12+o(1))n$ can be partitioned into vertex disjoint $\vec{T}_4$'s, and this
bound is asymptotically tight. We also improve the best known bound on the
minimum total degree for partitioning oriented graphs into vertex disjoint
$\vec{T}_k$'s.
