  A new derivation is given of four-point functions of charge $Q$ chiral
primary multiplets in N=4 supersymmetric Yang-Mills theory. A compact formula,
valid for arbitrary $Q$, is given which is manifestly superconformal and
analytic in the internal bosonic coordinates of analytic superspace. This
formula allows one to determine the spacetime four-point function of any four
component fields in the multiplets in terms of the four-point function of the
leading chiral primary fields. The leading term is expressed in terms of $1/2
Q(Q-1)$ functions of two conformal invariants and a number of single variable
functions. Crossing symmetry reduces the number of independent functions, while
the OPE implies that the single-variable functions arise from protected
operators and should therefore take their free form. This is the partial
non-renormalisation property of such four-point functions which can be viewed
as a consequence of the OPE and the non-renormalisation of three-point
functions of protected operators.
