  The total space of the spinor bundle on the four dimensional sphere S^4 is a
quaternionic line bundle that admits a metric of Spin(7) holonomy. We consider
octonionic Yang-Mills instanton on this eight dimensional gravitational
instanton. This is a higher dimensional generalization of (anti-)self-dual
instanton on the Eguchi-Hanson space.
  We propose an ansatz for Spin(7) Yang-Mills field and derive a system of
non-linear ordinary differential equations. The solutions are classified
according to the asymptotic behavior at infinity. We give a complete solution,
when the gauge group is reduced to a product of SU(2) subalgebras in Spin(7).
The existence of more general Spin(7) valued solutions can be seen by making an
asymptotic expansion.
