This is a centre for a comprehensive collection of Klee’s paintings, sculptures and forays into theatre, music and dance. Klee was born near Bern, so this is his monument. It has a rather larger auditorium than most other such places, but is basically your standard medium-sized art museum, a familiar enough genre. Piano has done some good ones in his time, so is scarcely new to the game. Perhaps he was bored. Perhaps he was too busy, as famous architects tend to be as they get older. But here he has resorted to lazy shape-making rather than the rigorous analysis for which he is known. He has fallen victim to icon syndrome.

He had an idea for a clever shape — a wave form in the landscape, a diminishing series of three linked buildings — and stuck to it. Being famous, he was allowed to get away with this. Unfortunately, the clever shape is not nearly so clever once you start to fit museum spaces into it. It is pretty much all wrong for its purpose, though rather beautiful and a structural tour de force. It is a long time since I’ve been to a place that displays art worse than this.

Consequently, the Zentrum Paul Klee summarises in one building the problem that has lurked in architecture ever since the Sydney Opera House competition of 1956: just because you can build something in an interestingly different shape, do you think you should? The answer to that is another question: what, exactly, do you want your cultural building to be? What is it for? Jorn Utzon’s Sydney Opera House succeeded triumphantly on the iconic level. Shame about its deficiencies as an opera house, but who cares? There is more than a touch of this landmark-first, function-second attitude to the Klee centre.

Bern is a small city. It plays third fiddle to cosmopolitan Zurich and Geneva. Basel and Lucerne are sparkier. Bern is seen as provincial, a capital in the bureaucratic sense only. Travel guides sometimes ignore it altogether — the ultimate slight. These are dangerous conditions for a new cultural building to take root in. People come to see it as a form of salvation. They imagine the tourist dollars. They think of Bilbao’s Guggenheim by Gehry. They are ready for the funny shape.

Well, I like funny-shaped buildings up to a point, and this one would make, I reckon, an excellent motor museum. Here is how it works. There are three thumbnail-shaped steel-arched buildings — large, medium and small — set in a row on a slight curve, each sloping down into the green hillside behind. Piano links the front facades in two ways: by sweeping each arch up to meet the next one, he succeeds in making that visual image of a wave in the landscape work; and by running a broad promenade behind the frontage along the full length of the building, he unites the three spaces with a linear lobby.

The problem comes when you try to work out what this three-humped edifice is for. Naturally, you assume the largest hump, the first one you see as you arrive, is the most important and must contain the art. No. It has the auditorium buried in the ground beneath it, but at ground level it is subdivided into various spaces, including a restaurant, what look like conference rooms, even a loading dock. All strangely disappointing.

So you walk on, and you find the art gallery is in the middle hump. There is a conventional flat-ceilinged temporary exhibition gallery downstairs that is rational and cool, but the main event, with the permanent collection, is upstairs. And you find that a big arched space, while it might have been great for giant contemporary installations, is really not very good for small early-20th- century paintings. There have to be walls to hang the paintings on, but fitting walls into a double- curving arched space is not easy. They are suspended from the ceiling and wobble slightly if you lean against them. The busy roof structure distracts you from the art. The paintings are diminished. Natural light has been all but banished.

It would have been nice — and not impossible — to get a sense of the sky through the roof without cooking the paintings. The engineers could have done it. The firm is Arup, which has made this awkward design work as well as it can. Arup has an unrivalled track record in getting difficult buildings built, including the Sydney Opera House, Piano and Rogers’s much earlier Pompidou Centre, and the series of radical architectural experiments represented by the annual Serpentine Gallery pavilions in London. It developed a wonderful natural-daylight system at IM Pei’s Richelieu Wing of the Louvre in Paris. But that daylight thing clearly wasn’t on the to-do list here, although Piano, it is said, tried for it. So, presumably, the curators are to blame. Whatever — as a consequence of this and its cul-de-sac shape, the Klee gallery is a lifeless space. I felt unhappy in there.

On to the third, smallest, hump. What’s this? It’s offices. Oh, well. And then you have to turn on your heel and go back the way you came. Because of the way the humps tail off into the hill, coupled with the unforgivingly rigid layout, you cannot walk out of the back of one space into the back of another. This is an architectural, rather than curatorial, blooper.

So much good architecture is about teasing you. The best buildings reveal themselves to you gradually. They bring you in at a tangent, take you through a low hall or round a tight corner and then, wham! — they give you the wow moment. Here, Piano gets this all wrong. You enter immediately into the biggest, most dramatic space, the linear lobby. After that, there is nothing better. Everything else is a spatial anticlimax, especially the main gallery.

My architectural hero has let me down badly. I’m hoping Piano hasn’t lost it altogether, particularly as he is developing plans for sundry buildings in London. I hate to say it, but it’s worth dropping in to see the Paul Klee centre because it is a beautifully made object lesson in precisely how not to design an art gallery.