A novel soybean cultivar, designated 0509240, is disclosed. The invention relates to the seeds of soybean cultivar 0509240, to the plants of soybean 0509240 and to methods for producing a soybean plant produced by crossing the cultivar 0509240 with itself or another soybean variety. The invention further relates to hybrid soybean seeds and plants produced by crossing the cultivar 0509240 with another soybean cultivar.