We investigate the magnetic properties of the Co4N (001) surface by using the full-potential linerized augmented plane-wave band method. We consider two possible terminations, i.e., Co-atomterminated and CoN-atom-terminated surfaces. From the calculations of the magnetic moment and the site-projected spin-polarized density of states of each atom in the systems, which remain very similar to the properties of the Co4N bulk structure, we nd that surface termination does not in uence considerably the magnetic properties of deeper layers in the anti-perovskite Co4N (001) surface. The properties of Co atoms in the two outermost layers depend on their position in the unit cell. CoI -type atoms, which are at the corners of a cubical unit cell, are distant from N atoms and they retain an isolated character as the Co atoms in Co fcc crystal. CoII -type atoms, which occupy the center of the cube faces, interact more strongly with neighboring N atoms. Therefore, the magnetic moment on CoII atoms is smaller than that on CoI atoms at the surface layer (S). Compared to the values of magnetic moments on the corresponding atoms in the bulk structure, the magnetic moments on the surface CoI(S) and CoII(S) atoms are larger: 2.01 and 1.55 B , respectively. In the CoN-terminated surface, the value obtained for CoII(S) is 1.61 B . The magnetic properties of the CoI atoms, which are barely in uenced by the presence of N atoms, do not depend much on the surface termination.