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The giant magneto-impedance (GMI) effect associated with the variation of transverse permeability for the ribbons Fe89Zr6Hf1B4 with different annealing temperatures TA = 793, 823, 893,923, 993, and 1033 K was investigated. There is an optimum annealing temperature TA ≈ 993 K for obtaining the largest GMI effect for the ribbons Fe89Zr6Hf1B4. The magneto-impedance GMI (Z) = (Z(H) - Z(O))/Z(O) for the ribbon with TA = 993 K can reach -55.09% at a frequency f =900 kHz under H = 7162 A/m. The relative changes of the real part of transverse permeability △μ’/μ’0 = (μ’(H)-μ’(O))/t’(O)under H = 7162 A·m-1 at f= 1 MHz are -78.83%, -89.98% and -94.77 % for Fe89Zr6Hf1B4 ribbons with TA = 823, 893,and 993 K, respectively. The strong GMI effect is accompanied by the large change of transverse permeability. A large magnetoreactance GMI(X) = (X (H) -X (O))/X (O) of-81.09% can be obtained at f= 100 kHz under H = 7162 A/m for the ribbon with TA = 993 K. Meanwhile, this present result gave an experimental support to the previous concept / assumption that the positive peak in the field dependence of magneto-impedance is connected to the peak of transverse permeability with varying fields.