The frequency dependence of magnetization process and giant magneto impedance (GMI) effect of Co-rich melt-extracted amorphous wires was studied by Kerr effect and impedance analyzer, respectively. It is demonstrated that the transverse Kerr intensity and the corresponding GMI response increase with increasing frequency, which contributes to the upgraded skin effect. However, the skin depth has a slothful trend with frequency when it is up to the megahertz range, which gives rise to the transformation of magnetization. The process is much more sensitive to the direct current magnetic field and the sensitive change of the circular permeability, and GMI response is observed as its consequence. This proves that the evolution of circumferential magnetization and the corresponding permeability with the direct current magnetic field is the essence of GMI response, and a much more sensitive magnetization promises a better GMI response.