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Frequency-modulated continuous-wave (FMCW) synthetic aperture radar (SAR) systems offer smaller size and lower cost compared with pulsed-mode systems. They are therefore widely used for Earth observation where frequent revisits at low costs or small sizes are desirable. By accurately formulating the instantaneous slant range during the transmitting and receiving operations, an analytical point target reference spectrum has been developed for the FMCW SAR system, where an additional range-azimuth coupling term is found. Based on previous work, this letter presents a modified inverse chirp-Z transform (ICZT) algorithm to deal with the range-azimuth coupling term, which appears to be a scaling factor in range. The new scaling factor is formulated in this letter for the first time. An ICZT is well suited for FMCW SAR since it can handle a dechirped signal without interpolations, thus reducing the computing load. Simulation experiment and real data processing result validate the proposed focusing algorithm.