The annealing effect on the magnetic and structural properties of Fe/Cu(100) ultrathin films has been studied. For films below 5 ML, their magnetization and Curie temperature are reduced considerably after annealing. We explain the reduction as a result of the transition from a high-moment ferromagnetic phase to a nonferromagnetic phase in the inner layers of the Fe films after annealing. Supporting evidence comes from the low-energy electron-diffraction study, which indicates a structural relaxation from a tetragonally distorted fct structure to a true fcc structure in the inner layers of the Fe films. The surface layers of the Fe films, after annealing, are still expanded, providing the main contribution to the remaining magnetization and nonzero Curie temperature of the annealed Fe films.