The effect of annealing on the magnetic properties and structural state of ribbons of a FeNiSiB amorphous alloy and of the alloy modified with copper is studied. The copper addition is shown to extend the temperature range of annealing that can be used to improve the magnetic properties of the alloy. The presence of copper changes the character of the onset of crystallization, namely, the volume, rather than the surface (like in the case of the copper-free alloy), crystallization is observed when the annealing temperature exceeds the temperatures corresponding to the optimum temperature range. © Pleiades Publising, Inc., 2006.