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Synthetic aperture radar (SAR) is an effective instrument for the formation of high-resolution images of the earth surface. Trajectory instability is one of the factors that affect the quality of the obtained images. The problem is that even in the case of application of a common motion compensation procedure, which is necessary for synthetic aperture formation, instabilities of the antenna beam orientation are still left uncompensated. This leads to radiometric distortions in SAR images. This problem is especially critical in the case of SAR processing with frame-based algorithms based on FFT (for example, the range-Doppler algorithm), which assume the constant antenna beam orientation within the large data blocks. In this paper the method of radiometric correction of SAR images is considered in the case of processing of SAR data in the frequency domain. Its idea is based on the formation of extended number of looks which corresponds to the broadening of the processed Doppler bandwidth. It is shown that such broadening allows to compensate the influence of two effects: changes of the real antenna beam orientation angles in respect to the aircraft velocity vector and also the possible additional broadening of the Doppler bandwidth of the received signals due to the application of the common motion compensation procedure. The obtained extended number of looks is used for the restoration of the multi-look SAR image without radiometric errors. The introduced methods of radiometric correction are an efficient alternative to expensive antenna stabilization systems and actively used in operating SAR systems. The efficiency of the developed algorithms is illustrated by real SAR data examples.