This paper presents a method to implement SAR slow-time space time adaptive processing (STAP) in the beamforming stage of the fast backprojection algorithm. This method is different from the recently published method where the SAR fast-time STAP is implemented after the beamforming stage for detection and then imaging. As a common SAR STAP method, the method proposed in this paper can be used for ground moving target indication (GMTI) and reconstruction of the image of the detected moving targets. The paper also presents some simulation results in order to illustrate the proposed method.