In this letter, a statistical edge detector based on the square successive difference of averages has been proposed and tested for SAR images. The operator employs the square successive of mean difference as the edge strength indicator for SAR images. It has been proved to be with constant false alarm rate and performs well in representation of many more region shapes. A postprocessing approach, including edge thinning and adaptive double-threshold processing, is proposed to refine the edge detection results. The performance of the proposed operator has been evaluated and compared with that of the Canny and ratio-of-average operators on simulated and real SAR images. The experimental results indicate that the operator achieves better performance in the detection rate and the localization accuracy, and the detected edges are more complete and longer than those by the other two operators.