This is the Italian side of the Matterhorn (or 'Cervino' to the Italians) and is more technical than Hornli ridge. 

Ascent to the Carrel hut:

From the Orionde refuge, follow the wide trail of the normal path of the Matterhorn which climbs up behind the building along ledges and steps until you reach the Croce Carrel. The track becomes less evident and you continue to climb easy rocks following the cairns and passing tracks. Reaching a ledge (snow at the beginning of the season) you go up aiming at the base of the obvious channel that cuts into the wall from right to left. Go up it with easy climbing, a short rope helps a more difficult step, up to climb back on more broken ground (danger of falling stones from above).

Climb to the right over leaning rocks up to a large snowfield which disappears late in the season. On snow or gravel, continue to climb slightly to the right, passing a step. Traverse to the right, and then climb again along a rocky ridge to a new snowfield on the ledge that cuts the upper part of the slope, below the east wall of the Lion's Head.

Cross to the right with some ups and downs, traces of passage (snow), always remaining close to the rock (spit) and reaching Colle del Leone on delicate terrain (3715 m, (12,188 ft) 6 h from Cervinia, 3 h from the Orionde Refuge).

The actual ridge begins from Colle del Leone. Climb to the right along the ridge (I), staying along the edge or on the Italian side. After a steeper stretch you climb more easily along the trail along the debris, quickly gaining altitude, until you get back to the ridge.Then you go up a more vertical section through compact rocks (I / II, then you reach the inclined slabs equipped with ropes. You then go up a more vertical section through compact rocks (I/II), then you reach the inclined slabs equipped with ropes (Placche Seiler). You go up to the right, then with easy passages (I) you reach a new cordon which overcomes a dihedral that ends on a comfortable terrace at the base of a vertical wall (La Cheminee).

This section was overcome with a fixed rope in a dihedral, but this collapsed in 2013 and now you have to climb the vertical wall directly, always equipped with ropes. The stretch is very tiring (10 m). Once out on a small terrace, an excellent stopping point, continue always following the rope for a small corner leaning to the left. At its end, a possible second stop can be set up. Then continue to the left and exit without difficulty (snow), quickly reaching Capanna Carrel (3,830 m, 1.5 h from Col del Leone, 8 h from Cervinia, 6 h from Plan Maison).g

The Lion Crest

Just behind the Capanna Carrel you reach the pitch where the Luigi Amedeo hut once stood and leads us to the start of the first canapone (Corda della Sveglia).

You pass the fairly vertical wall and a small roof with particularly tiring passages (chain), exiting on the rather wide ridge (shot). You then easily follow the cords to the right (keep), and then return to the comfortable ridge. A rope helps to overcome a short wall, beyond which one traverses to the right up to a short slab closed by a dihedral on the left. You pass it on the right (II) and continue more easily up to a new canapone. Follow it, passing a difficult overhanging passage to the right, often icy (Vallon des glacons, shot).

Once out on a ledge, follow it to the right up to a little man. Here you do not continue along the comfortable ledge but climb vertically by steps (I / II) in a gully up to a notch above the Grande Tour. The crest is very sharp (Crete du Coq) and you stay on the high Italian ledges (easy) up to a new notch. Climb some leaning slabs (Cretier slabs), then start a long traverse on the right side for a system of ledges (I / II), at times exposed (retains, numerous bolts), overcoming the Mouvais Pas (‘Bad, no?’), a difficult passage only in name. Continue the crossing passing under a smooth rock (Rocher des Ecritures- ‘Rock of the scriptures’), and descend to the snowy or icy slope of the Linceul. Climb the left side near the rocks (often hollow under the snow, keep it) and once the rock has been found, you will come within sight of the Grande Corde. You climb a first chain, then a long canapone with strenuous passages until you get back to the ridge (2 pitches). 

Climb the inclined slope of slabs for a long time (pitch / preserve depending on the conditions) which requires particular attention, especially if covered with snow (easy mixed passes), sometimes remaining on the Swiss side. After crossing the Cravate, a long ledge on the Italian side, you climb back to the top of Pic Tyndall (4,257 m (13,966 ft) 3 hours from Capanna Carrel).

Follow the flat ridge (snow), sometimes thin, for about 200 meters (Cresta Tyndall) overcoming some more delicate downhill sections. The last split section (Enjambee, aw-zhawm-bee, ‘spanned’) allows you to reach the hill that separates Pic Tyndall from the Testa del Cervino (0.30 h from Pic Tyndall, preserves).

From the hill you initially climb on the rocky edge, then remaining on the Italian side often on mixed / frozen terrain, looking for the best passages until you go up to the ridge on a small terrace, called Colle Felicite, named after the first woman who climbed here in 1867 ( retains / shoots depending on conditions). Continue to the left reaching the last set of fixed ropes. Follow it on exposed terrain (pitches) until you reach the base of the famous Jordan Staircase which you climb with strenuous climbing overcoming an overhanging stretch (shot). Immediately above, follow another rope (Corda Piovano) to the left up to a small ledge (Gite Wenworth, ‘zheat’). 

Remaining a little on the Swiss side, then climb back to the ridge (keep) and, following the ropes, you reach a new ledge (Pas Thioly), from which you can easily reach the Italian summit by snow (4,446 m, 14,586 ft, 2.5 h from Pic Tyndall, 5.5 h from the Carrel Hut). From the Italian peak, the small cross, you can reach the highest Swiss summit: first by descending a few meters, then by a beautiful exposed ridge, usually snowy (4.448 m, 14, 600 ft, 5 min from the Italian summit).

--translated from "Cervino--Valtournenche and Valle di Saint Barthélemy" by Andrea Greci &  Federico Rossetti 

Access

From Chatillon, follow the SR46 of Valtournenche to Cervivia. Cross the village and leave the car in the small parking lot at the end of Via Bich. If you go up by cable car, from the center of the village follow the signs for the ski lifts up to the large parking lots.

Approach

On foot, continue on the paved road. At its end, take the track that climbs to the left and soon reaches the dirt road. Follow it to the right with some hairpin bends up to the Capanna degli Alpini and continue to climb for a long time with a mountain path but with a wonderful view of the Matterhorn. Various tracks allow you to cut the hairpin bends and save a few minutes. Finally, we reach the large building of the Orionde-Duca degli Abruzzi Refuge (2810 m (9,219 ft), 2 h).

The refuge can also be reached by jeep with a paid service from Cervinia or alternatively you can also climb the first section of the Plateau Rosa lifts to Plan Maison (2550 m), saving an hour of walking and 500 meters of altitude.

From the arrival of the cable car, go up until you take the obvious road that cuts to the left. In a few minutes you will reach a crossroads and follow the path to the right on trail marker 65/14. Follow it on a slight slope with a splendid view of the Matterhorn pyramid and, losing a few meters of altitude, you reach an area of large boulders where you return to climb. Continue along the always evident path that cuts along the hillside. Going up the ridge of a moraine you quickly gain altitude, then go back to traverse to the left overcoming some brooks until you reach a small body of water and the adjacent Rifugio Orionde (1 hr from Plan Maison).

--translated from "Cervino--Valtournenche and Valle di Saint Barthélemy" by Andrea Greci &  Federico Rossetti

I climbed it all with just a full set of tri-cams and alpine draws but a few cams wouldn't go to waste.  A skinny 30m alpine rope did us just fine. And of course, ax & crampons are mandatory.