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The local potential measurement of an operating carbon nanotube transistor provides information on the defects in the nanotube and the interfacial potential barriers. While Kelvin-probe force microscopy is a powerful technique to measure the local surface potential, its accuracy is often degraded by the charges trapped on the surrounding insulator surface. Here, we introduce an alternative method to measure the local potential profile along the nanotube being less affected by those charges. We identified the location of a defect and detected the variation in the potential profile for different gate bias voltages, which were not detected by the conventional method.