Theoretical calculations are presented on a new hypothetical 3,4-connected carbon net (called squaroglitter) incorporating 1,4 cyclohexadiene units. The structure has tetragonal space group P4/mmm (No. 123) symmetry. The optimized geometry shows normal distances, except for some elongated bonds in the cyclobutane ring substructures in the network. Squaroglitter has an indirect bandgap of about 1.0 eV. The hypothetical lattice, whose density is close to graphite, is more stable than other 3,4-connected carbon nets. A relationship to a (4,4)nanotube is explored, as is a potential threading of the lattice with metal needles.