  We construct Yang-Mills connections on SO(n)-bundles over spheres equipped
with the Euclidean metric. We use a cohomogeneity one group action on the
bundle to reduce the Yang-Mills-equation to a system of ordinary differential
equations. The system is shown to have solutions by variational methods, using
ideas from harmonic map theory. Examples include Yang-Mills connections on each
of the countably many principal SO(6)-bundles over $S^6$, and countably many
Yang-Mills connections on $TS^n$ for $n\in\{5,...,9\}$.
