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This paper reports on the observation of localized state consisting of two filaments traveling straight in a dielectric barrier discharge in argon at atmospheric pressure. The localized state is different from that observed by Purwins, in which two pairs of spots travel along the system boundary. It travels straight along the diameter of active area mainly and rebounds at the system boundary, and therefore goes backwards and forwards in the active area. A model based on the alternate repulsive and attractive Coulomb forces is established and the interaction between the two filaments is analyzed. The study of the localized state is helpful to understand the soliton dynamics in nonlinear science.