The surface impedance tensor final_sigmâ is found for 120 μm diameter Co-based amorphous wires as a function of a dc axial magnetic field Hex. Contrary to the usual practice of giant magneto-impedance experiments, the voltage response is measured not only across the wire but also in the external coil (secondary coil), and the wire is subjected to an ac current flowing through it or the coil (primary coil), which allows all the components of the impedance tensor final_sigmazz, final_sigmaφφ and final_sigmazφ=final_sigmaφz to be determined. Under certain conditions, they all are very sensitive to Hex (especially final_sigmaφφ: 100–250%/Oe) but exhibit a different field behavior: the diagonal terms final_sigmazz and final_sigmaφφ are symmetrical with respect to Hex whereas the off-diagonal terms final_sigmazφ=final_sigmaφz are antisymmetrical, and at high frequencies, final_sigmazz has a minimum at Hex=0 where final_sigmaφφ has a maximum. The effect of a moderate dc bias current Ib is demonstrated to be favored for final_sigmazφ and final_sigmaφz, which are nearly zero for Ib=0. These new magneto-impedance characteristics may further expand the application opportunities for the GMI effect.