Abstract: Back Projection (BP) algorithm is suitable for airborne Ultra Wide Band Synthetic Aperture Radar (UWB SAR) imaging for its advantages such as perfect focusing and motion compensation. However, its application will be limited by the big computation load. The Sub-Image Fast Factorized Back Projection (SIFFBP) algorithm, which substantially reduces the computational load, can improve the practicability of the BP algorithm. In this article, an improved SIFFBP algorithm based on optimal regional partition is proposed by analyzing the regional division constraints. It provides a way to solve the acceleration-decline problem of the conventional SIFFBP algorithm when the SAR system has a small integration angle. Compared with the conventional algorithm, the proposal can further reduce the computational load when the integration angle is smaller than 90 degree or when the length of the imaging region is much larger or smaller than the width, While at the same time, it retains the same imaging precision. The performance of the proposal is demonstrated by using simulated data, as well as real SAR data collected by a P band airborne SAR.