Abstract: Method for repairing the teeth of a toothed ring gear, the method using a removable machining device, including a frame and a part moving with respect to the frame, supporting a cutting member, the method including: attaching the machining device to the toothed ring gear by tightening the machining device onto the ring gear in an attachment position on the ring gear with respect to the tooth to be machined; machining the tooth in an automated manner by control of the cutting organ following predetermined machining operations, in which the machining device is moved from an attachment position on the toothed ring gear corresponding to the previously machined tooth, to an attachment position of a neighboring tooth to be machined, while the toothed ring gear is stationary, the machining device being suspended and held by at least one tensioned cable connected to the frame of the rotating machine.