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In Landsat Thematic Mapper (TM) images, banding due to memory effect (ME) often appears every 16 lines at both sides of a bright object such as a cloud, which not only visually degrades the images but also makes quantitative analysis difficult. The ME is induced by an electric circuit connecting the detectors to the analog/digital converter. Based on the impulse response of the circuit, a restoration filter was proposed to correct the banding, but it must be truncated for improving computational efficiency. This paper proposes an efficient and exact correction algorithm by modeling an offset voltage of a preamplifier as a first-order differential equation. It is shown that the same impulse response is derived from the differential equation. As the differential equation can keep track of the offset voltage as a state variable, the ME of the preamplifier circuit can be corrected not only effectively but also seamlessly by taking the internal calibration interval and calibration lamp status into consideration. The parameters of the circuit are estimated from nighttime unprocessed TM data of 1996, and they are used to correct daytime data of the same year. It is shown that the proposed state-space approach is more computationally efficient than the previous restoration-filter approach.