Described is a machine (10) for debranching living trees. The machine can move up and down the tree autonomously by means of a drive mechanism and has an upper cutting unit comprising three blades (48, 50) and below it a lower cutting unit comprising two blades (46). The in total five blades (46, 48, 50) are arranged so that they cover the full girth of the tree. The two blades (46) in the lower cutting unit are horizontally offset so that their end portions can overlap. To move the machine (10) along the tree trunk there are two belt drives which press against the tree and are both driven by a single hydraulic motor (20). The upper cutting unit with its three blades (48, 50) can move horizontally as a whole, so that when the machine (10) 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 (46, 48, 50).