Abstract: According to the invention, unpurified biodiesel is brought in contact with cellulose-containing material by continuously and/or discontinuously mixing the same in order to eliminate the glycerin and catalyst residues, such as potassium soaps, accumulated during the production of the biodiesel. A system for carrying out said method comprises an agitated sedimentation tank (1) with a conduit (4,5) for delivering purified biodiesel into the agitated sedimentation tank (1) and a conveying device (6) for feeding cellulose-containing material into the agitated sedimentation tank (1). A drive unit (51) for an agitator (50) is disposed in the agitated sedimentation tank (1). A conduit (16, 20) extends from the agitated sedimentation tank (1) to at least one static sedimentation tank (2, 3). A valve (13) via which solid matter can be discharged from the agitated sedimentation tank (1) is mounted in the area of the bottom of the agitated sedimentation tank (1).