  We construct a classical solution of an Einstein-Yang-Mills system with a
fourth order term with respect to the field strength of the Yang-Mills field.
The solution provides a spontaneous compactification proposed by Cremmer and
Scherk; ten-dimensional space-time with a cosmological constant is compactified
to the four-dimensional Minkowski space with a six-dimensional sphere S^6 on
which an instanton solution exists. The radius of the sphere is not a modulus
but is determined by the gauge coupling and the four-derivative coupling
constants and the Newton's constant. We also construct a solution of
ten-dimensional theory without a cosmological constant compactified to AdS_4 x
S^6.
