Adsorption of half a monolayer of oxygen on the Rh(110) substrate gives a surface with a (2 x 2) p2mg symmetry structure, in which the substrate has a missing row (1 x 2) structure. He-beam scattering measurements show that close to 750 K this surface structure reversibly transforms into a phase of (1 x 2) symmetry. The phase transition has been classified as belonging to the order-disorder type, and falls into the 2D Ising universality class. Above the transition temperature proliferation of antiphase domain boundaries along the [001] direction is observed and discussed.