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We show that the spin connection of the standard metric on a six-dimensionalsphere gives an exact solution to the generalized self-dual equations suggestedby Tchrakian some years ago. We work on an SO(6) gauge theory with ahigher-derivative coupling term. The model consists of vector fields only. Thepseudo-energy is bound from below by a topological charge which is proportionalto the winding number of spatial S^5 around the internal space SO(6). The fifthhomotopy group of SO(6) is, indeed, Z. The coupling constant of higherderivative term is quadratic in the radius of the underlying space S^6.Comment: 7 pages, comments and a reference added, typos correcte

Classical solution in six-dimensional gauge theory with higher derivative coupling