A machine for stabilising palletised loads , comprising: - a functional arrangement provided with a reel of a covering tape , - a gripping device adapted to take a first end of the covering tape of the reel and to make it integral with the palletised load , - a first movement apparatus adapted to generate a relative motion of revolution of the functional arrangement around the palletised load , according to a predetermined revolution axis (Z), so as to unwind the covering tape from the reel and to wind it around the palletised load , - a second movement apparatus adapted to generate a relative motion of translation of the functional arrangement with respect to the palletised load in a direction parallel to the revolution axis (Z), so as to wind the covering tape , which continues to unwind from the reel , like a spiral around the palletised load , - a cutting device placed in the functional arrangement to separate the covering tape from the reel , and - a fixing device adapted to fix at least a second end of the covering tape to the palletised load , characterised in that the functional arrangement further comprises: - at least a first tensioning fin , which is adapted to rotate around an articulation axis (H) parallel to the axis (A) of the reel and is provided with a rectilinear end border , distal with respect to the articulation axis (H) and extending parallel to the articulation axis (H), which is adapted to stay in contact with a longitudinal edge of the covering tape unwinding from the reel , and - a first spring adapted to act on the first tensioning fin to push the end border thereof against said longitudinal edge of the covering tape . - a functional arrangement provided with a reel of a covering tape , - a gripping device adapted to take a first end of the covering tape of the reel and to make it integral with the palletised load , - a first movement apparatus adapted to generate a relative motion of revolution of the functional arrangement around the palletised load , according to a predetermined revolution axis (Z), so as to unwind the covering tape from the reel and to wind it around the palletised load , - a second movement apparatus adapted to generate a relative motion of translation of the functional arrangement with respect to the palletised load in a direction parallel to the revolution axis (Z), so as to wind the covering tape , which continues to unwind from the reel , like a spiral around the palletised load , - a cutting device placed in the functional arrangement to separate the covering tape from the reel , and - a fixing device adapted to fix at least a second end of the covering tape to the palletised load , - at least a first tensioning fin , which is adapted to rotate around an articulation axis (H) parallel to the axis (A) of the reel and is provided with a rectilinear end border , distal with respect to the articulation axis (H) and extending parallel to the articulation axis (H), which is adapted to stay in contact with a longitudinal edge of the covering tape unwinding from the reel , and - a first spring adapted to act on the first tensioning fin to push the end border thereof against said longitudinal edge of the covering tape . <EOS>