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Amorphous Co66Fe4B15Si15 ribbons were annealed at a temperature of 380°C for 8 h in open air under a field of 3 Oe applied along the sample axis. The annealed samples were etched in hydrofluoric acid solution during various times from 10 s to 30 min in order to the different thickness of material, tetch, from ribbon surface. The static permeabilities due to domain wall motion μs,dw and magnetization rotation μs,rot are separated from the permeability extracted from the magnetoimpedance spectra. For the samples with thickness tetch less than 2 μm, both μs,dw and μs,rot are nearly zero at H=-3 Oe, while they are relatively large at H=+3 Oe. As the etched thickness increases over 2 μm, μs,dw and μs,rot at H=-3 Oe start to increases and eventually reach similar values to those at H=+3 Oe. The variations of μs,rot and μs,rot with tetch reflect that the sample annealed in open air is nearly saturated in the direction opposite to that of annealing field. This is due to antiferromagnetic coupling between the inner amorphous phase and the surface crystalline phase with thickness about 2 μm.