Asymmetrical giant magnetoimpedance (AGMI), which utilizes a high frequency bias field hb, is realized in a Co-based amorphous wire having a circumferential anisotropy in the outer region. No asymmetry in the dc magnetic configuration is needed in this case. AGMI is discussed in terms of the surface impedance tensor, demonstrating that the effect of hb is related to the role of the off-diagonal component of the impedance in the voltage response measured across the wire. This effect is important for developing autobiased linear magnetic sensors. Using two oppositely biased wires, a near-linear voltage output (±4 mV) is obtained in the range of ±5 Oe for the sensed dc field at a frequency of 8 MHz.