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For a synthetic aperture radar (SAR) onboard a platform with a rectilinear track, the range history of a point target can be accurately expressed hyperbolically. The track can be curvilinear for a maneuverable SAR platform. The hyperbolic equation becomes inadequate, and an expression with high-order terms is needed. Using the method of series reversion, we derived the 2-D spectrum for the return signal of the curvilinear SAR. There were five independent variables in the spectrum, but available imaging algorithms could only handle three in the focusing using the spectrum. Thus, a variable-decoupling method was developed to reparameterize the initial spectrum so that only three variables remained. After the incorporation of the decoupling method into the chirp-scaling algorithm, simulations of the SAR with a curvilinear track were studied. Promising results were obtained.