The magnetic properties of ${\mathrm{Na}}_{5}{\mathrm{RbCu}}_{4}({\mathrm{AsO}}_{4}{)}_{4}{\mathrm{Cl}}_{2}$ are reported. The material has a layered structure comprised of square ${\mathrm{Cu}}_{4}{\mathrm{O}}_{4}$ tetramers. The Cu ions are divalent and the system behaves as a low-dimensional $S=1/2$ antiferromagnet. Spin exchange in ${\mathrm{Na}}_{5}{\mathrm{RbCu}}_{4}({\mathrm{AsO}}_{4}{)}_{4}{\mathrm{Cl}}_{2}$ appears to be quasi-two-dimensional and nonfrustrated. Measurements of the bulk magnetic susceptibility and heat capacity are consistent with low-dimensional magnetism. The compound has an interesting, low-entropy, magnetic transition at $T=17 \mathrm{K}.$