The impedance of an amorphous Fe4.3Co68.2Si12.5B15 wire (100 μm diameter) exhibits an extraordinarily large frequency dependent resistance in addition to the previously reported frequency dependent wire reactance. The frequency response of both the resistance and reactance is almost entirely suppressed by an axial magnetic field HA<150 Oe, resulting in a typical magnetoresistance for frequencies f<1 MHz of the order of the dc wire resistance. The magnetoresistance at f=1 MHz is ΔR/Rsat=370%. As the bulk of the magnetic response occurs for HA<5 Oe, this system shows great technological promise. We give a quantitative analysis of the phenomenon, which is rooted in classical electrodynamics.