Sputtered Co/Cu multilayers of different wavelength modulation have been prepared over different substrates. The study of Co layers by X-ray absorption spectroscopy shows that a significant change in the cobalt environment happens when the Cu thickness is smaller than 20 Angstrom. This result is in agreement with a non layer-by-layer growth mode of cobalt over copper, which means that Co-films consist of disconnected islands. The dependence of some physical properties at this copper thickness range will be regarded as the basis of this local arrangement of Co.