We report the magnetic measurement for oxygen adsorbed on different substrates at low coverage. An intriguing behavior of the oxygen magnetization against the applied magnetic field has been found. We demonstrate that it is an interplay between the substrate orientation of oxygen molecules and a weak antiferromagnetism of unit spins occurring via the substrate that shows such a behavior. The conclusion is made that the interaction of the oxygen molecules with the substrate (being neglected in previous work) plays a crucial role on the physical properties of the system.