Abstract We have performed a scanning tunneling microscopy study on a grid-like mesoscopic pattern formed by nitrogen adsorption on a Cu(001) surface. Two types of boundaries are present between square-shaped N-adsorbed islands: a fine straight line of monoatomic width (“monoatomic line”) and a bare Cu(001) belt of several atoms wide (“multiatomic belt”). The boundary type depends on whether c(2 × 2) protrusions in neighboring islands are aligned in-phase or out-of-phase across the boundary. Considering that an adsorbed N atom prefers to be coordinated by four Cu atoms on a plane and that the topmost Cu layer is expanded by 2–3% by N adsorption, we propose the missing-Cu-atom model for a monoatomic line where a single Cu row is ejected by a compressive stress exerted from neighboring N-islands. The reconstruction maintains the planar 4-fold coordination of Cu atoms to an N atom in the case of in-phase alignment, and relieves the N-induced compressive stress very efficiently. Whereas, the Cu row ejection would destroy the stable local structure in the out-of-phase case. The N-induced compressive stress is relieved in the other mechanism where it is compensated with a tensile stress in a bare Cu(001) region. The region is imaged as a multiatomic belt. The above models for a monoatomic line and a multiatomic belt explain well various features observed in the grid pattern. Moreover, the missing-Cu-atom model rationalizes the attractive interaction between N-islands which was difficult to understand in a traditional, elasticity-based view on the self-organization.