Processing by stress-annealing (450 MPa, 300 °C, 1 h) the glass-coated microwire of Fe75B9Si12C4 composition a macroscopic magnetic anisotropy with a circular component is developed. This anisotropy very significantly improves the giant magnetoimpedance (GMI) effect with respect to the observed in the as-prepared microwire. The analysis of the GMI response as a function of the frequency (10–1000 MHz) opens new lights to understand the distribution of the magnetic anisotropy inside the glass-coated microwire. We have investigated the GMI response of the stress-annealed Fe75B9Si12C4 glass-coated microwire. From the frequency dependence of the GMI we have analyzed the distribution of the magnetic anisotropy inside the metallic nucleus obtaining good agreement with the average value of the anisotropy field deduced from the hysteresis loop of the bulk. From measured magnetic field dependences of GMI ratio we evaluated the frequency and magnetic field dependences of the penetration depth. We found that the minimum penetration depth of Fe75B9Si12C4 microwire decreases from about 1.5 μm down to 0.8 μm after stress annealing. Obtained dependences demonstrate that the minimum penetration depth value as well as the frequency and magnetic field dependences are considerably affected by the stress-annealing. Display omitted •Preparation of thick glass-coated amorphous microwires.•Improvement of GMI effect of microwires by -annealing.•Fast single domain wall propagation with domain wall mobility of about 11,9 m2/As.•Enhancement of domain wall propagation by annealing.•Change of Hysteresis loop of microwires from rectangular to linear after stress annealing.