  We show that the spin connection of the standard metric on a six-dimensional
sphere gives an exact solution to the generalized self-dual equations suggested
by Tchrakian some years ago. We work on an SO(6) gauge theory with a
higher-derivative coupling term. The model consists of vector fields only. The
pseudo-energy is bound from below by a topological charge which is proportional
to the winding number of spatial S^5 around the internal space SO(6). The fifth
homotopy group of SO(6) is, indeed, Z. The coupling constant of higher
derivative term is quadratic in the radius of the underlying space S^6.
