A method of making an amorphous alloy ribbon according to the present disclosure includes: preparing an amorphous alloy ribbon having a composition composed of Fe, Si, B, C and inevitable impurities (hereinafter, "alloy ribbon"); and, in a state where the amorphous alloy ribbon is tensioned with a tensile stress in the range of 5 MPa to 100 MPa, increasing a temperature of the amorphous alloy ribbon to a maximum target temperature ranging from 410 ° C to 480 ° C, with an average temperature increase rate ranging from 50 ° C / s to less than 800 ° C / s and lowering a temperature of the thus heated amorphous alloy ribbon from the maximum target temperature to a temperature of a heat transfer medium for lowering the temperature average rate of temperature reduction ranging from 120 ° C / s to less than 600 ° C / s, wherein increasing the temperature as the temperature is raised and decreasing a temperature as the temperature is decreased by allowing the alloy ribbon to be in a tensioned state moves, and the moving tape alloy tape with a heat transfer is brought into contact with the medium and an alloy ribbon with a composition FeBSiC is produced (a, b: atomic proportion in the composition, c: atomic proportion of C with respect to a total of 100.0 atomic% of Fe, Si and B, 13.0 atom -% ≤ a ≤ 16.0 atom%, 2.5 atom% ≤ b ≤ 5.0 atom%, 0.20 atom% ≤ c ≤ 0.35 atom% and 79.0 atom% ≤ (100-ab) ≤ 83.0 atomic%).
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