We present a new technique for inferring neutral densities in the Martian upper atmosphere from atmospheric absorption of magnetically reflected solar wind electrons. Using electron loss cone measurements from the Magnetometer/Electron Reflectometer (MAG/ER) experiment on board Mars Global Surveyor (MGS), we derive upper thermospheric (~160--230 km altitude) densities in the southern hemisphere from 160¿ to 200¿E at 2am local time, continuously from 1999 to 2005. We find a mean density of 0.027 kg/km3 at 160 km and observe a latitude-dependent, repeatable seasonal variation of a factor of 1.8--4, with inter-annual differences and consistently lower winter densities at 50¿--55¿S, compared with 0¿--30¿S. The mean densities, overall seasonal variation and latitude dependence are in general agreement with the Mars Thermosphere Global Circulation Model (MTGCM). These measurements are important for improved understanding of the dynamics of Mars' upper atmosphere and for planning spacecraft aerobraking maneuvers.