It wasn't split into two, it was split into 4, and later became two.

The allies divided up Germany (and Austria) each into 4 sectors (American, British, French, and Soviet). However, they also decided that Berlin so was important, they they would also split Berlin into 4 sectors as well, despite it being inside of the Soviet sector.

Eventually, the American, British, and French sectors of Germany combined to form a singular West Germany, this included their sectors of Berlin as well. The Soviet Sector, including their part of Berlin, became East Germany.