The detection of liquid water by the Mars Advanced Radar for Subsurface and Ionosphere Sounding (MARSIS) at the base of the south polar layered deposits in Ultimi Scopuli has reinvigorated the debate about the origin and stability of liquid water under present-day Martian conditions. To establish the extent of subglacial water in this region, we acquired new data, achieving extended radar coverage over the study area. Here, we present and discuss the results obtained by a new method of analysis of the complete MARSIS dataset, based on signal processing procedures usually applied to terrestrial polar ice sheets. Our results strengthen the claim of the detection of a liquid water body at Ultimi Scopuli and indicate the presence of other wet areas nearby. We suggest that the waters are hypersaline perchlorate brines, known to form at Martian polar regions and thought to survive for an extended period of time on a geological scale at below-eutectic temperatures.