This paper proposes a coordinate-transform (CT) implementation for the fast factorized backprojection (FFBP) algorithm (CT-FFBP) to process high-resolution spotlight synthetic aperture radar (SAR) data. Unlike the FFBP utilizing two-dimensional image-domain interpolation for sub-aperture fusion, CT-FFBP finishes the image-projection using CT with the accommodation of chirp-z transform and circular shifting. Without interpolation, CT-FFBP yields enhanced efficiency over the interpolation based FFBP, besides maintaining high precision simultaneously. Both simulation and real-data experiments verifies the efficiency and precision superiorities of the CT-FFBP.