ac magnetoresistance (MR) measurements performed in thin ribbons of the amorphous soft ferromagnet Co70.4Fe4.6Si15B10 are reported with a longitudinal dc applied magnetic field H varying from 0 to ±15 Oe. The dependence of the MR with the frequency f of the measuring ac current was investigated for 0.4≤f≤100 kHz. No significant frequency dependence in the resistivity ρ for H=0 and H=±15 Oe was found. For intermediate values of H, ρ(H) presents a peak in H which increases linearly in frequency. The MR peak in H at room temperature varies from typical values of 0.13% in the low-frequency range to a giant value of 27% at 100 kHz. Two possible sources for the frequency dependence of the magnetoresistance in amorphous alloys are discussed.