Start heading down due north until you get to the Matterhorn trail crossing (S). Take a left down a path which remains pretty much flat until Furggsee Lake (1).
Then go down a slight hill towards Hirli gondola lift upper station (2). Head east bypassing Scharzsee Hamlet Lake , you'll come across another gondola lift, take the trail to the left. Cross the Hirli gondola lift line near high point 2500 (3). Carry on, heading west before taking the trail to the right leading to Hirli lower station (4).
After several twists and turns, walk along a large path reaching a trail crossing which leads to Zmuttbach River dam (5).
Take this trail which is on the left, cross over the dam and take the trail to the right leading to Zmutt village (6), reaching an access ramp towards Tour du Cervin.
Take the ramp (7) leading to Zermatt and the Youth Hostile (8), and that's it for today.