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Schöndorf was a fairly large settlement (about 2300 inhabitants) in the old Austria-Hungary Empire. It was in Temes megye (county), járás (district) of Újarad, and was known by its Hungarian name as Szépfalu. The majority of the people in Szépfalu were of German ethnicity and of the Roman Catholic faith. They did have a church within this settlement and the LDS FHL does have church records on microfilm for the years 1766-1836.
Szépfalu, Temes, Hungary, also called Schöndorf, Sefdin, and Sardinu, is now Frumuseni in Romania.
To find the Settlement of Szépfalu on an old map of the Austria-Hungary empire go to this site: http://lazarus.elte.hu/hun/maps/1910/vmlista.htm and download the map of Temes. Be patient, as these are large maps and take awhile to load. To find Szépfalu, scroll across the top to the 30' line of longitude, then down to where the "pink" area begins. Szépfalu is just to the left of here. On my current map of Romania (I got mine at Barnes and Nobles) the modern day settlement of Frumuseni is just below the large city of Arad. Hope this answers your question ahd helps to get you started in tracing your heritage. Good luck! Suzanne