Antiparallel water-water interaction is a significant interaction between two water molecules and plays an important role in liquid water. The potential energy surface of antiparallel water-water interaction was calculated at accurate CCSD(T)/CBS level of theory by systematic changes of the torsion angle THOHO, parallel displacement r, normal distance R, and water-water dihedral angle Pa/Pb. The results show that the most stable geometry of antiparallel water-water interaction has an interaction energy of −4.22 kcal/mol and THOHO = 140°. A significant portion of the antiparallel interactions have interaction energies more negative than −2.0 kcal/mol. The angle α of the most stable geometries of antiparallel water-water interactions is in the range 110°–120°. Comparison with classical hydrogen bonds in water dimers shows that hydrogen bonds with values of angle α < 140° have interaction energies up to −3.2 kcal/mol, while a significant number of antiparallel water-water interactions is stronger than it. The antiparallel geometry is a low barrier transition state between two hydrogen bonded minima with changed acceptor–donor roles of two water molecules.