The magnetization of an iron film deposited on a noble metal in the presence of an external field is measured as the thickness is continually increased atomic layer by layer. The increment of magnetic moment per additional atom of deposited iron approaches the bulk value at three layers, but two of the layers remain nonmagnetic independent of film thickness. No explanation is offered for the existence of the two nonmagnetic layers, but the observed magnetization of the additional layers is explained quantitatively by a spin-wave theory which includes anisotropy energy. © 1969 The American Physical Society.