We revisited the structure of monolayer iron nitride islands grown on Cu(001) using the well-established procedure, i.e. by bombarding the substrate with low-energy N+ ions, depositing Fe at room temperature and annealing in ultra-high vacuum (UHV). The geometric parameters of the obtained iron nitride were matching those of the “Fe2N” phase described in the literature and constituting the middle-plane-cut of the γ′-Fe4N unit cell. However, the atomic structure was found to exhibit an out-of-plane corrugation not reported by other authors so far. Moreover, the islands had an Fe1.3N stoichiometry and were characterized by a much higher work function value than the one predicted theoretically for the Fe2N phase. Based on these findings, we propose a new structural model for monolayer iron nitride on Cu(001), in which an additional N atom resides on top of every second Fe atom in each atomic row of the Fe2N. We also show that the Fe1.33N islands may be reduced to species with Fe2N stoichiometry through the exposure to O2 at room temperature and subsequent annealing in UHV. Thus, direct formation of the Fe2N phase under specific experimental conditions, as indicated by other authors, may be also possible.