  We develop an iterative algorithm for the genus expansion of the hermitian
$N\times N$ one-matrix model ( = the Penner model in an external field). By
introducing moments of the external field, we prove that the genus $g$
contribution to the $m$-loop correlator depends only on $3g-2+m$ lower moments
($3g-2$ for the partition function). We present the explicit results for the
partition function and the one-loop correlator in genus one. We compare the
correlators for the hermitian one-matrix model with those at zero momenta for
$c=1$ CFT and show an agreement of the one-loop correlators for genus zero.
