A method of producing an amorphous alloy ribbon having a composition of Fe100-a-bBaSibCc (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-a-b)≤83.0 atom %) includes: preparing an alloy ribbon; and, in a state in which the alloy ribbon is tensioned with a tensile stress of from 5 MPa to 100 MPa, increasing a temperature of the alloy ribbon to from 410° C. to 480° C., at an average temperature increase rate of from 50° C./sec to less than 800° C./sec, and decreasing a temperature of the thus heated alloy ribbon to a temperature of a heat transfer medium for temperature-decreasing, at an average temperature decrease rate of from 120° C./sec to less than 600° C./sec, wherein the temperature increase and decrease are performed by contacting the traveling alloy ribbon with a heat transfer medium.