An innovative polymeric membrane has been invented, which presents a breakthrough in the field of desalination membranes. It can desalinate simulated seawater of exceptionally high concentration to produce a high flux of potable water with over 99.7% salt rejection (%SR) in a once-through purge-air pervaporation (PV) process. A set-up was constructed for conducting the desalination experiments and the effect of initial salt solution concentration (Ci) and pervaporation temperature (Tpv) on the water flux (J), %SR, separation factor, and pervaporation separation index were determined. The membrane was prepared by the phase-inversion technique, of a specially formulated casting solution consisting of five ingredients, after which the membrane was subjected to a post-treatment by which certain properties were conferred. The results confirmed that the salinity of the pervaporate was independent of Ci (all %SR above 99.7). The best result was at Tpv = 70 °C, where J varied from 5.97 to 3.45 l/m2 h for Ci = 40–140 g NaCl/l, respectively. The membrane morphology was confirmed to be asymmetric. The contact angle was immeasurable, indicating the membrane to be super-hydrophilic. Activation energies computed using Arrhenius law were, under all conditions investigated, less than 20 kJ/mol K.