Self-assembled MnN nanoislands have been prepared on Cu(001) substrate. The nanoislands show a square shape and a well-defined size. They are regularly arrayed with a periodicity of (3.5+/-0.1) nanometer and form a two-dimensional square superstructure. The MnN island superstructure is stabilized by a short-range mechanism. A structural model has been proposed to explain the self-assembly and the high quality of the superstructure.