Polarimetric synthetic aperture radar (SAR) systems require verification and calibration of their polarimetric performance after launch. Dual-antenna calibration transponders with freely rotatable, linearly-polarized antennas are one of the most common calibration targets for this task. Because the transponders are used as a measurement standard, any misorientation of the polarization direction of the transponder antennas leads to characterization errors for the SAR instrument. In this paper, we present a novel calibration approach with which the polarization direction of linearly polarized antennas can be accurately determined; no additional reference antenna with a previously known polarization is required. The novel approach will reduce polarimetric transponder calibration errors in the future and will lead to a higher accuracy in calibrated, fully polarimetric SAR systems.