In this paper, an improved range-interpolation-free polar format algorithm (PFA) is proposed for the bistatic synthetic aperture radar (SAR). As an alternative solution to the range spatial frequency resampling of the classic bistatic PFA, the conventional range-frequency scaling transformation (CRST) provides a further explanation of the range resampling of the bistatic PFA from the perspective of range-azimuth decoupling. Nevertheless, CRST cannot be taken as the perfect equivalence to the range resampling of the PFA for its inalterable output spacing of the range spatial frequency. Besides, CRST can be implemented by the principle of chirp scaling (PCS). The scaled range frequency may exceed the observed frequency band, which will cause range spectrum aliasing. To solve the above problems, we propose an improved range-frequency scaling transformation (IRST), which has the same alterable range spatial frequency output spacing as the classic PFA. Further, the PCS-based IRST is also given. The aliased spectrum localization criterion is defined to avoid spectrum aliasing according to the relation between the range frequency and the observed frequency band after IRST. Analyses and simulations are executed to demonstrate the effects of the proposed algorithm.