A machine for debranching living trees can move up and down the tree autonomously via a drive mechanism and has an upper cutting unit including three blades and below it a lower cutting unit including two blades. The in total five blades are arranged so that they cover the full girth of the tree. The two blades in the lower cutting unit are horizontally offset so that their end portions can overlap. To move the machine along the tree trunk there are two belt drives which press against the tree and are both driven by a single hydraulic motor. The upper cutting unit with its three blades can move horizontally as a whole, so that when the machine is moved and encounters thicker or slightly bent parts of the tree trunk it can give way in order to prevent the bark from being damaged by the blades.