  The form factor of the unitary group U(N) endowed with the Haar measure
characterizes the correlations within the spectrum of a typical unitary matrix.
It can be decomposed into a sum over pairs of ``periodic orbits'', where by
periodic orbit we understand any sequence of matrix indices. From here the
diagonal approximation can be defined in the usual fashion as a sum only over
pairs of identical orbits. We prove that as we take the dimension $N$ to
infinity, the diagonal approximation becomes ``exact'', that is converges to
the full form factor.
