Magnetization behavior of ultrathin (3 ML) epitaxial Co(001) films on Cu(1 1 13) terraced surfaces was studied in situ using magneto-optic Kerr effect. The films show easy magnetization along the steps. Unusual hard axis Kerr loops (H perpendicular to the steps and in the surface plane) are observed near room temperature and evolve at higher temperature (127-degrees-C) toward the soft magnetic behavior more typical of the easy axis loops observed on the same films. A model is postulated for the behavior that includes a fourfold in-plane anisotropy and a uniaxial in-plane anisotropy of possibly magnetoelastic (ME) or magnetostatic (MS) origin.