  We show that, although the correlator of four stress-tensor multiplets in N=4
SYM is known to have radiative corrections, certain linear combinations of its
components are protected from perturbative renormalisation and remain at their
free-field values. This result is valid for weak as well as for strong coupling
and for any gauge group. Our argument uses Intriligator's insertion formula,
and includes a proof that the possible contact term contributions cannot change
the form of the amplitudes. Combining this new non-renormalisation theorem with
Maldacena's conjecture allows us to make a prediction for the structure of the
corresponding correlator in AdS supergravity. This is verified by first
considerably simplifying the strong coupling expression obtained by recent
supergravity calculations, and then showing that it does indeed exhibit the
expected structure.
