We report the observation of an interference between the electric dipole (E1) and the magnetic quadrupole (M2) amplitudes for the linear polarization of the Ly-α1 (2p3/2→1s1/2) radiation of hydrogenlike uranium. This multipole mixing arises from the coupling of the ion to different multipole components of the radiation field. Our observation indicates a significant depolarization of the Ly-α1 radiation due to the E1-M2 amplitude mixing. It proves that a combined measurement of the linear polarization and of the angular distribution enables a very precise determination of the ratio of the E1 and the M2 transition amplitudes and the corresponding transition rates without any assumptions concerning the population mechanism for the 2p3/2 state.