We left Zermatt via the funicular railway that goes up to Sunnega. That's where the real starting point is. To go down, take the train at Riffelalp to return to Zermatt.
(S) From the funicular exit, take the path that branches off to the left, climbing along a concrete parapet. It more or less follows the cable car that goes up to Blauherd and is lined with wooden sculptures representing local wildlife.
(1) As you approach the cable car terminus, whose building is visible just above, leave the path that climbs up to it and take the path that continues level to the right. Follow this path until you meet another path that winds its way up below.
(2) Note the intersection, which you will come across again on the way down, and continue straight on towards Lake Stelissee.
(3) This small lake reflects the summit of the Rimpfischorn, which towers over the Fluealp refuge, visible above the lake.
Go around the lake and descend the track that crosses its spillway. Further down, this track meets another track. Follow it to the right until you reach the path you took on the way up. Turn left and follow this path up to the fork you spotted and already passed on the way up.
(2) Start the descent down the switchbacks on the left. At each crossroads, follow the direction of Grindjisee. At the last switchback, the direction is not indicated, but the line of stones laid across the slope, visible from the previous crossroads, is the path to follow. (If you miss it, don't worry. You'll catch up a little further on, having lengthened the route. The paths are well marked and you can't go wrong.) At the bottom of the cliff, you'll finally discover Lake Grindjisee, nestled in its green setting.
(4) Cross the lake's spillway and join the track on the right that descends nearby. Follow it around the end of the glacial moraine and descend into what was the bed of the glacier not so long ago. At the bottom of the descent, turn right to cross the stream and climb up the opposite slope.
(5) At the next trail junction, take the path that climbs opposite until, after a few more bends, it joins a cross trail. Follow this trail to the right until you find the path on the left that climbs towards Gruensee. As you approach the lake, follow a wooden pipe that increases the water supply to this lake, which is much needed.
(6) Walk along the right-hand side of the lake and continue straight on towards Ze Seewjinen, the large inn at the end of the plateau.
(7) From the restaurant, take the path towards Riffelalp. After crossing a scree slope, the path enters a forest where you will notice old larch trees with twisted trunks, many of which have been struck by lightning. You will come to a fork in the path.
(8) Leave the path to Findeln on your right and continue straight ahead until you go around the rocky outcrop that closes off the Balmbrunne ravine.
(9) Cross the stream and continue through the woods. You will come out onto the impressive ledge path that goes around the cliff, then descend to Rifelalp station, where the train will be waiting to take you down (E).