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In this letter, a fast backprojection algorithm (FBPA) is proposed for bistatic synthetic aperture radar imaging. For range compression, the signal recorded by the synchronization channel of the receiver on the ground is used as a matched filter to compress the echo signal. This method can reduce the requirements of satellite-orbit measurement and synchronization precision. For azimuth compression, a secondary phase correction is implemented to reduce the effect caused by the approximation involved in the FBPA. The computational complexity of the proposed algorithm is O(N2.5). The proposed algorithm is applied in a graphics processing unit and verified by simulation and real raw data.