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A self-organization phenomenon has been found in a dielectric-barrier discharge (DBD) excited by a piezoelectric transformer (PT). In order to investigate the phenomenon, the DBD is generated in helium and argon using an electrode arrangement that consists of the PT surface inducing high voltage and a soda glass with indium tin oxide evaporated as a transparently conductive back electrode. The observation is performed by varying the gas pressure with a constant applied voltage of the PT. It is found that the formation of self-organized patterns in both helium and argon requires a small amount of air admixed. The discharge regime depends upon the gas pressure between 50 and 1400 torr, and the organized patterns in argon appeared only in the gas-pressure range of 100-250 torr.