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For a synthetic aperture radar (SAR) onboard a geosynchronous-earth-orbit (GEO) satellite, the track can be curvilinear. Thus, the validity of imaging algorithms based on the conventional hyperbolic range equation (CHRE) becomes questionable. A fourth-order range equation is adopted to improve the accuracy in the approximation of the range history for GEO SAR and a modified chirp scaling algorithm (CSA) is proposed. Simulation results show that the presented algorithm has better performance than the CHRE-based CSA in the GEO case, implying good application prospects.