It is demonstrated through computer simulations that a cyclotron autoresonance maser (CARM) amplifier with finite output pulse width operated in a high‐order waveguide mode, such as the TE01mode, is feasible. This is because the absolute instability grows from the initial beam noise fluctuation and takes a certain time interval to become disruptive to the desired amplification process. A drive wave with sufficiently high intensity can further reduce the growth rate of the absolute instability and prolong the stable amplification period.