  Four point functions of general N=4 1/2-BPS primary fields, satisfying the
next-next-to-extremality condition
\Delta_{1}+\Delta_{2}+\Delta_{3}-\Delta_{4}=4 are studied at large N and strong
coupling. We apply new techniques to evaluate the effective couplings in
supergravity, and confirm that the four derivative couplings arising in the
five-dimensional supergravity vanish on-shell. We then show that the four point
amplitude resulting from supergravity naturally splits into a "free" and an
interactive part which resembles an effective quartic interaction. The precise
structure agrees with superconformal symmetry and supports the conjecture
formulated by Dolan, Osborn and Nirschl regarding the strongly coupled form of
four point correlators of chiral primary operators. We also evaluate the
amplitude in large N free field SYM theory and discuss the results in the
context of the correspondence.
