It is an exhilarating, if nerve-racking, achievement.
Yet for Pippa Middleton it is an adventure tinged with sadness, too.
The 32-year-old made the climb in honour of the younger brother of her fiance James Matthews, whose life was lost when a Himalayan storm engulfed his assault on Everest in 1999.
For that emotional reason, her husband-to-be chose not come with her, though he shares her devotion to extreme sports.
Instead Pippa, a writer and party planner, was supported by her brother James Middleton, 29. The pair hope to raise thousands of pounds for the charity set up in the name of her fiance's brother, Michael.
Just hours after her descent, Pippa spoke movingly about what had inspired her - and how she was longing to share her adventure with her fiance.
She told The Mail on Sunday: 'It was humbling to have been able to climb one of the world's most beautiful mountains and raise money for a charity created in memory of an extraordinary young man who lost his life on another peak. Although I have raised money in the past for the Michael Matthews Foundation, it has now become even more important to me and my family.
'Although neither I nor my brother ever met Michael, we both share his spirit and passion for the mountains. We made this climb knowing he would have been there nudging us on, and we are honoured to be supporting his memory.'
She added: 'It would have been good if my fiance James had been here to share the experience, something I know he would have loved to have done. Mountain climbing, though, has disturbing memories and understandably James kept his feet firmly on the ground, while giving us his complete support.'
The Duchess of Cambridge's sister is known for her physical fitness and adventurous spirit and has already conquered Mont Blanc, swum the Bosphorus in Istanbul and cycled across America.
But the challenges of the jagged pyramid of the Matterhorn, which rears up above the Swiss ski resort of Zermatt, are greater than anything she has ever faced.
Each year, the mountain claims three or four lives and was one of the last in Europe to be conquered.
It was a passion for the world's peaks that beckoned Michael from a promising City job to Everest, where he became the youngest Briton to reach the summit in 1999.
But while he was still in the so-called 'Death Zone' - everything from around 26,000ft above sea level, where the air is too thin to sustain human life - he was torn from his path and his guide by a snowstorm.
The foundation founded in his name gives children in some of the world's remotest places an education. It operates in countries including Burma, Thailand, Nepal and Tanzania, building schools which double as health centres and community hubs.
Much of the fund raising has been done by James Matthews through sports events. His surviving brother, the Made In Chelsea star Spencer Matthews, has said: 'The loss was heartbreaking for James. With just a year and a half between them, he and Mike were the closest of friends.'
The Middletons travelled to Zermatt last week and acclimatised by climbing the 4,000m peak known as Breithorn on Thursday.
The next day, they left for the Hörnli Hut, the Matterhorn's historic base camp where they had a dinner of veal and polenta, followed by a chocolate whipped dessert before an early night.
They woke at 3am yesterday, had breakfast at 3.30am and left at 3.50am on a path with a sheer drop on each side, lit only by torches strapped to their helmets. Roped to guides, they reached the Solvay Hut 4,000m up on the north-eastern ridge, to take on water as the sun rose.
Pippa revealed: 'We found ourselves scrambling up the rock using our hands as well as our feet, having to be deft at navigating around protruding rocks and learning how to trust our feet, our crampons, and above all, our guide.
'The climb was in every way exhilarating, each step taking us a little further from our comfort zone, with lactic acid building in our thighs, a light head from the altitude and a dry mouth resulting from a combination of fear, adrenaline and dehydration.
'For all that, my brother and I have loved it. Not only do we have the same ethos but we look after each other.'
It was 7.30am when, as they neared the peak, they were pictured jumping for joy. They spent just 15 minutes there before starting the equally treacherous descent, which requires climbers to abseil down sheer rock faces.
For James Matthews, it must have been a bittersweet moment: the sight of his fiancee standing triumphant on a mountain with her sibling, ensuring his own little brother never fades from memory.
