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In this paper, a noncontact linear positioner based on superconducting magnetic levitation for high-precision positioning has been tested under cryogenic conditions (similar to 20 K and similar to 10(-6) Pa). The prototype is able to achieve submicrometric positioning resolution of 230 +/- 30 nm RMS along a stroke of +/- 9 mm length with a current resolution of 15 mu A, and a peak current requirement lower than +/- 500 mA. In addition, it was demonstrated that an open-loop control strategy could be used for positioning the moving part with the accuracy of the order of 1 mu m. On the other hand, deviations of the slider position were found to be +/- 650 mu rad for the pitch, lower than 100 mu rad for the yaw, +/- 2000 mu rad for the roll, and +/- 4 mu m for the lateral run, all of them related to a full stroke motion. These results reveal a good performance of the device and demonstrate the potential of a new tool for applications, where high-precision positioning is required within a long range in cryogenic environments like far-infrared interferometry.