  The coupled cluster method (CCM) is a method of quantum many-body theory that
may provide accurate results for the ground-state properties of lattice quantum
spin systems even in the presence of strong frustration and for lattices of
arbitrary spatial dimensionality. Here we present a significant extension of
the method by introducing a new approach that allows an efficient
parallelization of computer codes that carry out ``high-order'' CCM
calculations. We find that we are able to extend such CCM calculations by an
order of magnitude higher than ever before utilized in a high-order CCM
calculation for an antiferromagnet. Furthermore, we use only a relatively
modest number of processors, namely, eight. Such very high-order CCM
calculations are possible {\it only} by using such a parallelized approach. An
illustration of the new approach is presented for the ground-state properties
of a highly frustrated two-dimensional magnetic material, CaV$_4$O$_9$. Our
best results for the ground-state energy and sublattice magnetization for the
pure nearest-neighbor model are given by $E_g/N=-0.5534$ and $M=0.19$,
respectively, and we predict that there is no N\'eel ordering in the region
$0.2 \le J_2/J_1 \le 0.7$. These results are shown to be in excellent agreement
with the best results of other approximate methods.
