The accident occurred on Tuesday lunchtime as the group began their descent from the 4000 metre summit of the Lagginhorn, the Swiss Blick tabloid newspaper said on Wednesday.
“There were two fathers with grown up sons and an underage daughter, they were all Germans. The sons were around 20 years old,” a mountain shelter employee told the paper.
A further member of the group had turned back shortly before the incident, said police, due to an “uneasy” feeling which ended up saving his life. The man had to watch from below as the other five members of his party simultaneously slipped from the path and fell 400 metres to their deaths.
“According to the first indications we have to assume that they were tied together by a rope as they walked,” police spokesman Renato Kalbermatten told Blick. “Otherwise they wouldn’t have all fallen at the same time.”
“For me there are only two explanations for the accident. Either it was an avalanche that dragged them down to their deaths. Or one of the group slipped and pulled the others with them on the rope,” added mountain guide and head of the rescue party Rolf Trachsel.
The Germans tackled the peak - said to be the easiest of the Valais range nicknamed the "four-thousanders" - without the help of a local guide.
The mountain has been the scene of several accidents in recent years, claiming the lives of two German and two Italian walkers since 2009.