The study of the Co environment in Co/Cu multilayers by X-ray absorption spectroscopy shows that a significant change in the cobalt environment occurs when the Cu thickness is smaller than 20 Angstrom. Data are explained in terms of an island structure of the Co layers. This result agrees with a non layer-by-layer growth mode of cobalt over copper. The temperature dependence of the magnetization presents also differences for these samples according to the structural behavior.