The magnetic permeability and giant magnetoimpedance effect of Fe73.5Cu1Mo3Si13.5B9 alloy ribbons in different annealed states have been measured as functions of the external magnetic field and the ac driving current frequency. It is found that the giant magnetoimpedance effect in the magnetic-field annealed state is larger than that in the nonfield annealed state. In the field annealed state, the easy magnetization direction is along the driving current as well as the external magnetic field. This leads to significant change of the permeability at high frequencies, and consequently the magnetoimpedance is enhanced in this state. © 1997 American Institute of Physics.