Compared with the original backprojection (BP) algorithm, the fast factorized BP algorithm accelerates enormously. As it is known to all, 2-D image interpolations are always utilized to raise the accuracy, yet leadings to the tradeoff with the efficiency. In this paper, a novel factorized BP algorithm based on Cartesian coordinate without interpolation, is proposed for high-resolution spotlight SAR with much better efficiency and accuracy. The innovative idea is achieved by establishing two spectrum compressing filters to decrease the cross-range Nyquist sampling rate enormously, thus avoid spectrum aliasing. The proposed algorithm, termed as the Cartesian factorized BP (CFBP) algorithm, can produce images with the similar quality as the BP does, but is better than FFBP, where the interpolations accumulate errors to some extent. The CFBP is designed for spotlight mode working in both the linear and curved trajectories. Simulation results and real-data processing validate the superiorities of CFBP by the comparisons with FFBP and the original BP individually.