The Sentinel-1A satellite was launched in April 2014 with a primary C-Band terrain observation with progressive scans synthetic aperture radar (TOPSAR) onboard and has collected plenty of high-quality images for global change studies. However, low magnitude signals around image margins (black margins) does not preserve the normal standard level, influencing the potential usage with these data. Through image analysis, we find that the signal from black margin (BM) is highly dominated by the closest effective signals and the signal in BM shows an increasing trend along the direction from image boundary to image center. An edge detector is developed based on the signal characteristics of BM. Furthermore, an automatic method to discriminate and eliminate BM is designed. Images from both extra wide (EW) and interferometric wide (IW) swath observation modes, covering the land, ocean, and coast of the Antarctic, are taken to verify the robustness of our method. Through comparison with BM edges extracted by human interpretation, our method has the maximum BM edge extraction error of 1.9 ± 3.2 pixels. When considering perimeter (or area) difference along radial direction of BM edge, our method has an averaging extraction accuracy of −0.35 ± 0.11 (or 0.14 ± 1.38) pixels, which suggests that our method is effective and can be potentially used to eliminate BM for multidisciplinary applications of Sentinel-1 data.