  We describe an iterative scheme which allows us to calculate any multi-loop
correlator for the complex matrix model to any genus using only the first in
the chain of loop equations. The method works for a completely general
potential and the results contain no explicit reference to the couplings. The
genus $g$ contribution to the $m$--loop correlator depends on a finite number
of parameters, namely at most $4g-2+m$. We find the generating functional
explicitly up to genus three. We show as well that the model is equivalent to
an external field problem for the complex matrix model with a logarithmic
potential.
