  We report structural and magnetic properties of the spin-$\frac12$ quantum
antiferromagnet Cu[C$_6$H$_2$(COO)$_4$][C$_2$H$_5$NH$_3$]$_2$ by means of
single-crystal x-ray diffraction, magnetization, heat capacity, and electron
spin resonance (ESR) measurements on polycrystalline samples, as well as
band-structure calculations. The triclinic crystal structure of this compound
features CuO$_4$ plaquette units connected into a two-dimensional framework
through anions of the pyromellitic acid [C$_6$H$_2$(COO)$_4$]$^{4-}$. The
ethylamine cations [C$_2$H$_5$NH$_3]^+$ are located between the layers and act
as spacers. Magnetic susceptibility and heat capacity measurements establish a
quasi-two-dimensional, weakly anisotropic and non-frustrated spin-$\frac12$
square lattice with the ratio of the couplings $J_a/J_c\simeq 0.7$ along the
$a$ and $c$ directions, respectively. No clear signatures of the long-range
magnetic order are seen in thermodynamic measurements down to 1.8\,K. However,
the gradual broadening of the ESR line suggests that magnetic ordering occurs
at lower temperatures. Leading magnetic couplings are mediated by the organic
anion of the pyromellitic acid and exhibit a non-trivial dependence on the
Cu--Cu distance, with the stronger coupling between those Cu atoms that are
further apart.
