  We construct the complete and explicit non-linear Kaluza-Klein ansatz for
deriving the bosonic sector of N=4 SU(2)\times U(1) gauged five-dimensional
supergravity from the reduction of type IIB supergravity on S^5. This provides
the first complete example of such an S^5 reduction that includes non-abelian
gauge fields, and it allows any bosonic solution of the five-dimensional N=4
gauged theory to be embedded in D=10.
