Separation and discharge of contaminants and defibration of undefibered waste paper can be effected in a single apparatus which has a generally cylindrical casing, a rotor concentrically arranged in the casing and a cylindrical main screen plate concentrically surrounding the rotor. Stock is separated by the main screen plate into that passing from inside through the main screen plate to outside and that not passing through it. The stock passing through the main screen plate is sent as accept stock to a next process. The stock not passing through the main screen plate is passed through a gap of a defibering section provided by defibration stator and rotor for defibration of undefibered waste paper and is further separated into the stock passing through an auxiliary screen plate and that not passing through it. The stock passing through the auxiliary screen plate is sent back through a circulation pathway in the rotor to inside of the main screen plate. Only the stock not passing through the auxiliary screen plate is discharged out of the system as the reject.