Symmetric self-organized discharge filaments have been observed in the rf ͑500 kHz͒ dielectric barrier discharge of Ar gas between two parallel quartz plates with a MgO film. The arrangement of the filaments is confined around the center on the quartz plate plane. With increasing voltage, the number of filaments increases, and the area of filament arrangement also increases. The arrangement of the filaments does not move if the quartz plate with a MgO film is employed, while the whole arrangement rotates without a MgO film. According to the results of current-voltage measurements, Lorentz attractive force is much smaller than Coulomb repulsive force. This suggests that a confinement potential exists as in the case of two-dimensional Coulomb systems in a parabolic potential. However, some of the filament arrangements do not match to those for charged particles in the Coulomb systems, which suggests that the confinement potential does not have pure parabolic profile.