Longitudinal and transverse magnetoresistivity measurements have been performed on a-Fe40-xNi40MnxB12Si8 alloys (0<or=x<or=5.5) in fields up to 40 kG, at 4.2 K, 100 K, 200 K, and 300 K. Above technical saturation, all the alloys exhibit a negative slope, i.e. the resistivity decreases as a function of the magnetic field. The high-field magnetoresistivity slope becomes more and more negative with increasing Mn concentration. Assuming that the negative slope of magnetoresistance is caused by the suppression of spin waves, the temperature and composition dependence of magnetoresistivity of the present series could be qualitatively understood. The spin-wave contribution to the zero-field resistivity has been estimated using a simplified approach. Furthermore, the ferromagnetic anisotropy of resistivity (FAR) has been calculated and the results are analysed in the light of a two-current conduction model generalized to weak ferromagnets and amorphous alloys.