Theoretical and computational study for a polarization change of localized and finite amplitude Alfve´n waves propagating parallel to an applied magnetic field is presented using both reductive perturbation theory and numerical simulations. In the magnetohydrodynamic limit (&ohgr;≪&OHgr;i) where right‐ and left‐hand circularly polarized waves are degenerate, one of the transverse components of the circularly polarized Alfve´n wave is stable as it propagates, but the other component is unstable to either self‐focusing or diffraction effects. Consequently, the wave changes its polarization from circular to linear. In the high frequency regime (&ohgr;≳&OHgr;i), where two circularly polarized waves (right‐ and left‐hand circularly polarized waves) are not degenerate, two transverse components of the circularly polarized Alfve´n wave are strongly coupled to each other, and there is almost no polarization change.