Many reasons have been put forward to explain away the brighter palette and decorative flattening of Matisse's post-First World War canvases. Clement Greenberg, the American critic, saw them as symptoms of what he called the "flight into pastoral", a euphemism for the new taste for prettiness that followed the Great War. Others have claimed rivalry with Picasso as the cause. This exhibition, however, suggests a different reason: the months the artist spent in Morocco in 1912-13 imbibing the decorative forms of Arabic art. Matisse's flirtation with the Fauves had already begun to push him away from figurative painting and towards a preoccupation with two-dimensional decoration; Islamic art lent this decoration a religious element.
One the most impressive things about this intelligent show is that its curators have resisted the urge to overstate their case. Islamic decoration was not the first exotic art-form to have caught Matisse's eye. Work done in Moscow for the merchant collectors Ivan Morosov and Sergei Shchukin had already exposed the painter to the hieratical style of Russian icon painting. The Institut's show sensibly owns up to this, pointing out both the obvious iconic influences and the Russian folk-art traits in works like La Petite Mulatresse (1912). In fact, the pictures Matisse painted while actually in Tangier are a strange hybrid. Works like Sur la Terrasse, the middle panel of his Moroccan Triptych, are Russianised renditions of Moroccan scenes: a nod, perhaps, to the taste of Morosov, for whom the paintings were intended.
At the same time, though, something new was happening in Matisse's Moroccan canvases. Look again at the female subject in La Petite Mulatresse - she is Zorah, Matisse's favourite model - and you will see a growing interest in the relationship between the human form and the space in which it is set; or, put another way, between figuration and decoration. In Sur la Terrasse, the figure still reigns supreme; the room in which Zorah sits is realistically articulated in space, and left bare-walled so as to not to detract from Matisse's subject. Decorative objects are three-dimensional: a bowl of goldfish and a pair of slippers, classical repoussoir elements used to draw the eye back into the picture space and the figure it contains.
In La Petite Mulatresse, by contrast, any idea of three-dimensionality has gone out of the window. Now, the figure is linked to the flattened picture space only by a repetition of decorative devices on both, the red dots on Zorah's girdle being picked up by dots on the blue ground behind her.
The rest, as the Institut du Monde Arabe sagely refrains from saying, is history. If the number of works Matisse painted in Tangier is small, their influence on his subsequent work is enormous. Look at a picture like Figure decorative sur fond ornamental, painted back in Nice in 1925- 26, and you will see the working-out of a formula first experimented with in Morocco more than a decade before. Matisse may have insisted that he was "only ever interested in the figure", but the form of that interest has clearly changed since Tangier. The female nude in Figure decorative can hardly be said to be the picture's subject. Rather the opposite: what she is, as her name suggests, is a piece of decoration like any other in the work, only rather less so. By Odalisque debout au brasero, painted in 1929 - odalisques were another important souvenir of the painter's time in Tangier - Matisse has almost done away with the female figure altogether, reducing her to a transparent wash, a kind of painterly Cheshire Cat.
Or not. The Institut's convincing reading of the post-Moroccan evolution in Matisse's style is not that it erased the human form from his work so much as that it translated it into a set of decorative elements. Poor Matisse could not win. In France, he was ridiculed for painting anything as old-fashioned as an odalisque, a staple of Ingres and Delacroix; in America, he was burnt in effigy for painting anything as salacious. Actually, Matisse's female nudes are neither of those things. What they are is pretty: decorative figures that evolve over the years into decorative forms.
Look at a late work like the stencilled Nu aux bas verts, made two years before the artist's death in 1954, and you find the female figure reinvented as a vegetal one, arms blending imperceptibly into branches. The inspiration is clearly from Islamic art, which discourages the direct representation of the human form. Les Abeilles (1948) also shows Matisse's growing fondness for using cut paper in making art, another throwback to his earlier interest in Moorish tiles. Seen in this context, the late, great project for the stained glass of the chapel in Vence seems as much the outcome of an Islamic aesthetic as of a Christian one: a novel view, but one that this show argues absolutely compellingly.
Institut du Monde Arabe, Paris (00 33 1 40 51 38 38), to 30 Jan