False alarms (FAs) pose a major challenge for operational ship detection in spaceborne Synthetic Aperture Radar (SAR) imagery. This paper presents a novel algorithm for identification and tracking of FAs in repeat-pass Radar Constellation Mission (RCM) imagery. The algorithm benefits from that not only ambiguities but also fixed ocean structures and small islands are recurrently detected at predetermined geographic locations in the repeat-pass acquisitions. Efficacy of the proposed algorithm is demonstrated through tracking an azimuth ambiguity, a small island, and an elevation grating lobe range ambiguity in a stack of twenty-six Ship Detection RCM images acquired near Galapagos Islands.