  The coupled cluster method is applied to a spin-half model at zero
temperature ($T=0$), which interpolates between Heisenberg antiferromagnets
(HAF's) on a kagome and a square lattice. With respect to an underlying
triangular lattice the strengths of the Heisenberg bonds joining the
nearest-neighbor (NN) kagome sites are $J_{1} \geq 0$ along two of the
equivalent directions and $J_{2} \geq 0$ along the third. Sites connected by
$J_{2}$ bonds are themselves connected to the missing NN non-kagome sites of
the triangular lattice by bonds of strength $J_{1}' \geq 0$. When
$J_{1}'=J_{1}$ and $J_{2}=0$ the model reduces to the square-lattice HAF. The
magnetic ordering of the system is investigated and its $T=0$ phase diagram
discussed. Results for the kagome HAF limit are among the best available.
