In the crystal structure of the synthetically prepared title compound, [Cu(C14H12N2)2](C4HO4) x 0.5H2O or [Cu(dmphen)2](HSq) x 0.5H2O (dmphen is 2,9-dimethyl-1,10-phenanthroline or neocuproine and HSq is hydrogen squarate), the Cu(I) centre has distorted tetrahedral coordination geometry comprised of four N atoms from two bidentate dmphen ligands. The squarate monoanions form a ten-membered dimer, graph set R(2)(2)(10), linked by two strong intermolecular O-H...O hydrogen bonds. These squarate dimers are linked into chains that propagate along the [100] direction. An extensive three-dimensional network of C-H...O hydrogen bonds and pi-pi interactions is responsible for stabilization of the crystal structure.