The range migration algorithm (RMA) is an accurate imaging method for processing synthetic aperture radar (SAR) signals. However, this algorithm requires a big amount of computation when performing Stolt mapping. In high squint and wide beamwidth imaging, this operation also requires big memory size to store the result spectrum after Stolt mapping because the spectrum will be significantly expanded. A modified Stolt mapping that does not expand the signal spectrum while still maintains the processing accuracy is proposed in this paper to improve the efficiency of the RMA when processing frequency modulated continuous wave (FMCW) SAR signals. The modified RMA has roughly the same computational load and required the same memory size as the range Doppler algorithm (RDA) when processing FMCW SAR data. In extreme cases when the original spectrum is significantly modified by the Stolt mapping, the modified RMA achieves better focusing quality than the traditional RMA. Simulation and real data is used to verify the performance of the proposed RMA.