The authors predict the presence of symmetric-antisymmetric oscillations of the magnetoplasmon energy as a function of magnetic field in a double-quantum-well structure. Because electrons in the localized states cannot effectively screen the scattering potential from the impurities, in a strong magnetic field, the Landau-level width increases much faster than the square root B dependence in a weak field. As the barrier width increases, the oscillation peaks at the smaller odd integral filling factors are smeared out before those at the larger odd integral filling factors. This leads to the quenching of the symmetric-antisymmetric magnetoplasmon oscillation peaks.