  In a string calculation to order $\alpha'^3$, we compute an eight-derivative
four-dilaton term in the type IIB effective action. Following the AdS
prescription, we compute the order $(g_{YM}^2N_c)^{-3/2}$ correction to the
four-point correlation function involving the operator $tr F^2$ in four
dimensional N=4 super Yang-Mills using the string corrected type IIB action
extending the work of Freedman et al. (hep-th/9808006). In the limit where two
of the Yang-Mills operators approach each other, we find that our correction to
the four-point correlation functions develops a logarithmic singularity. We
discuss the possible cancellation of this logarithmic singularities by
conjecturing new terms in the type IIB effective action.
