Ground moving target indication (GMTI) is one of the important applications of synthetic aperture radar (SAR). This paper introduces a GMTI method for local detection of the ground moving targets in SAR image based on normalized relative speed (NRS) hypotheses. The input of the GMTI method is a complex SAR image where areas of interest for GMTI are locally selected. The output of the method includes the detected targets, the NRSs with respect to the SAR platform, the locations where the detected targets are focused, and the SAR images of the detected targets. The mathematical background of the GMTI method is presented in detail. The method is validated with the data delivered by the Coherent All-Radio Band Sensor, an airborne ultrawideband-ultrawidebeam low-frequency SAR system. The shortcomings of the introduced method are investigated and followed with the solutions. IEEE