From the Konkordia Hut descend the ladders then head NE onto the centre of the Grünegg glacier. Next head N, more steeply, passing beneath pt 3476m, looking for a snowy gully that leads steeply up to the ridge above. Climb this (40 degrees) to the broad snowy shoulder. Follow the easy snowy slope above until easy mixed or rocky scrambling to the summit of the Grünegghorn. Downclimb to the L a short section of rock and snow to the col between the Grünegghorn and the Gross Grünhorn. This can be tricky if icy.

From here the quickest route is to keep to the glacier to the L of the ridge until about halfway up, at about 3900m. Then cut back R to the ridge itself where pleasant scrambling, involving moves of UIAA 2, lead you to the summit. The views are amazing of all the surrounding 4000m peaks, and particularly impressive is looking down on the huge expanse of glaciers all around. Descent is the same in reverse.

There is a rappel descent which some people take, direct down from the saddle between the Gross Grünhorn and the Grünegghorn. This is very loose, a frequent scene of accidents, hence not recommended, despite the apparent ease of going this way to access the Finsteraarhorn Hut.