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CoFeNiCrSiB amorphous ribbons have been prepared by rapid quenching and subjected to the post preparation heat treatments in air. Structure, magnetic properties and giant magnetoimpedance (MI) characteristics were investigated. Short annealing of the sample at 380°С for 4 min leads to a useful structural relaxation and the highest MI ratio ΔZ/Z =350% for the total impedance. In as prepared state “two-peak” MI field dependences were well correlating with effective magnetic anisotropy features. Post preparation treatment resulted in clear transformation into “one-peak” shaped MI curve typical for the ribbons with longitudinal effective anisotropy. Corresponding decrease of the field sensitivity by the order of magnitude as a result of short heat treatments in air shows their importance.