With this route, you can take a quick detour to Schwarzsee where you will find the Matterhorn sign with which you can take pictures. You would also see the Matterhorn from a different angle from here.
Zermatt to Furi : Walk or take a bus to Zermatt Bergbahnen, the cable car station located at the southern end of Zermatt. From here, ride the gondola to Furi.
Furi to Schwarzsee : Take a quick detour and view the Matterhorn from a different perspective by taking a cable car to Schwarzsee from Furi which takes roughly 8 minutes.
Schwarzsee to Trockener Steg : Ride another gondola from Schwarzsee for another 9 minutes to reach to Trockener Steg.
Trockener Steg to Matterhorn Glacier Paradise : From Trockener Steg, take a futuristic cable car to reach the summit. This ride is about 8 minutes.