We investigate the relaxation effects of magnetization modulus and precession axis on the damping time of the precession in L10-ordered FePt alloy film using a time-resolved magneto-optical Kerr effect. It is revealed that their fast relaxation processes during the precession bring about the overestimation of the damping time of the precession. We found that this error becomes more significant as the pump intensity increases. We propose that these corrections need to be considered for materials with the fast relaxation dynamics during the precession. (C) 2017 Elsevier B.V. All rights reserved.