The giant magneto-impedance (MI) effect and magnetic permeability of alloy ribbons were measured as a function of the annealing temperature. When the ribbons had been annealed at the optimum temperature () they exhibited both a large MI and excellent soft magnetic properties. The MI was also calculated on the basis of classical electromagnetic theory. It was found that a large change in the effective magnetic permeability, caused by the application of an external magnetic field in an excellent soft magnetic sample, was crucial for the MI effect. Furthermore, the effect of the resistivity on the MI was also investigated. When the resistivity decreases, the eddy current losses increase and the frequency at which the variation in the complex impedance exhibits its maximum moves to a low value; thus the sample exhibts a large MI effect.