We present here a moving target detection method so-called local detection of moving target by focusing. The term local implies that the method only works with areas of interest but not whole SAR scene whereas the term focusing indicates that the method is based on the concept of relative movement. The mathematical background of the method is presented in details. The introduced method is then examined with simulated and experimental SAR data to evaluate the method as well as to show the practicality of the method. The reference SAR system for this study is CARABAS, an airborne UWB low frequency SAR system. The method shows a number of advantages in comparison to the original version.