  We present new estimates of the spatial two-point correlation function of
rich clusters of galaxies selected from the APM Galaxy Survey. We have measured
redshifts for a sample of $364$ clusters out to a depth of $\sim 450\hmpc$. The
clusters have a mean space density of $\bar{n} = 3.4\times 10^{-5}\hmpccc$. The
two-point correlation function, $\xi_{cc}$, for this sample is equal to unity
at a pair-separation of $r_0 = 14.3\pm1.75\hmpc$ (2$\sigma$ errors), consistent
with our earlier results from a smaller sample. The new observations provide an
accurate determination of the shape of $\xi_{cc}$ to pair-separations of about
$50\hmpc$. Our results show that $\xi_{cc}$ has a higher amplitude than
expected according to the standard $\Omega=1$ cold dark matter (CDM) model on
spatial scales $2\simlt s \simlt 50\hmpc$, but are in good agreement with
scale-invariant fluctuations in either a low density CDM model or a critical
density universe made up of a mixture of hot and cold dark matter. Our results
provide strong constraints on so called `co-operative' models of galaxy
formation in which the galaxy formation process introduces large-scale
structure in the galaxy distribution.
