The present invention relates to a prior application U.S. Ser. No. 11/705,116 > wherein a flat rectangular extension (122) is added to protect from wear the skittle of a snowmobile ski when crossing rocky paths. The flat extension is used as floating link between the guide and the tail (131) of a wear runner laid out longitudinally of the ski. The guide (120) located at the front of the ski is always engaged, along with the self-sharpening runner, in ice, while the extension (122) keeps the back of the ski flat. The extension may be of a reversed U-shape comprising an extra web (135) and two extra cutting wings (136) protruding from the web (135) to a certain depth in direction of the ground and longitudinally of the extension, thus defining five cutting trails.