Spin precessions in the stripes of alpha-MnAs films prepared on GaAs(001) are investigated using an all-optical pump-probe method. We find that a large-angle spin precession appears while the stripe width decreases. In addition, the large-angle precession considerably changes the resonance frequency, resulting in a significant decrease in the relaxation time. These changes in the precessional motion are mainly ascribed to the dephasing of the nonuniform spin waves existing at the large-angle precession, as experimentally confirmed by varying the precession angle via tuning pump fluence. Micromagnetic simulations using a single Gilbert damping constant well predict the experimental observations, which verifies the interpretation of the change in the precessional motion.