Vive la Peinture!!! Amitis Matisse. This exultant battle cry is sprawled over a postcard addressed to Monsieur P. Bonnard art peintre. Matisse jotted it down when he came out of a museum in Amsterdam on 13 August 1925. The piercing slogan was the start of an exchange of 62 letters between the two finest artists of the last century which would last until 1946, a year before Bonnards death.

This exhibition draws its inspiration from the shy and secretly exuberant exchange of thoughts on art by two calmly bourgeois French artists. Though formal, attentive to decorum and cool on the surface, you can sense a deep, warm respect and mutual admiration when you study the few pages in the glass cases on view here.

The huge catalogue prints all the letters the two men wrote to each other with such disarming plainness and humble sagacity about their views on art that they put all the latter-day critics included in it to shame. Maddeningly they are only in Italian.

Bonnard to Matisse: I think of you as a spirit stripped of all aesthetic conventions the one thing that permits you to look straight at nature is the greatest fortune that can befall a painter thanks to you I benefit a little for this Matisse to Bonnard: Your letter found me absolutely hopeless I did not deserve your compliments even if they coincide with my aims actually something conventional is paralysing me my drawing and my painting wont come together. My drawing is my thing, it knows how to make what I feel particular. But my painting is messed up by my own new conventions: flat colour, no shadows, no modelling painting and drawing are supposed to act on one another to express light and spiritual space Im not able to do it drawing by a colourist is not a painting but your words have done me good because they make me try to merit them

When the weather is fine but cool there is a mist of vermilion in the orange shadows and of violet in the greys, Bonnard writes to Matisse. In my morning walks I amuse myself by trying to define the various aspects of landscape as space, as intimacy, as decoration I see different things every day in the sky, the objects everything changes all the time, you could drown in it Matisse to Bonnard: The light that filters into half-shuttered hotel rooms. It simmers from below like on a stage. All is false, absurd, extraordinary, delicious.

They do not much mention illness, private feelings or the harsh reality of the war raging around them. We should keep worries and hurts to ourselves so we can convey the beauty of the world with the joy of painting, wrote Matisse. The truth is that a painter exists only when he has a palette in his hand and he does what he can.

The bad news about this show is that as usual the uncomfortable architecture of the Vittoriano is crowded with lesser works due to its obscure logistics. Even if they come from the worlds most prestigious museums there are too few great breakthrough pieces.

The good news is that rarely seen works have been found, that some make illuminating parallels to major ones we all know, and truly that in the end even the studio sweepings are splendid. Both artists were too noble to ever go entirely wrong and create anything less than entrancing.

We have long had an image of these seminal artists as coming from different periods. Bonnard seemed to be still a late impressionist, while Matisse was resolutely avantgarde. In fact they were born within two years of one another, Matisse the older. Bonnard was part of the Nabis group which was into posters and timely decorative work at the turn of the century, and because he had immediate commercial success, he became known to the general public early. Matisse did not find his way until a decade later, when he joined the Fauves. Both Matisse and Bonnard were long overshadowed by that art-history-devouring monolith, Picasso.

Bonnard built his oils with the perseverance of a sea creature they are like coral beds. Tiny tufty touches of the brush accumulate into a stippled fabric of nacreous paint interlaced with shadows of opalescent purple. Matisse invented great, even, chunky shreds of colour poppy and geranium red, gauloise blue, tart yellow, uniform green cradled by sooty line and patterns. One seems subtly mysterious, the other boldly direct.

They came from middle-class backgrounds and middle-northern France with its muted skies. In mid-career the Midi shocked them into a new awareness. The revelation of the noon of a sun-drenched world pierced by sharp shadows, swift changes from dark to dazzling brightness, pushed them to burst into shameless colour. They were never the same again after they went to live down south by the shores of the Mediterranean. And despite their differences in approach, they were united by a deep bond: they looked at nature before them and tried to translate it into a spiritual expression.

Look at Bonnard here: early Paris squares brimming with vivacious shoppers; sails set in sea-blue like chips of shell; the white cubes of Cannes nestling under a thunderously violet horizon; gardens shimmering with herbaceous greens, butter-cup yellows, lilac, Tiepolo rose, sudden red gashes and the pearl-grey of clouds; Marthe, gleaming wet fresh from her bath; himself, almost disembodied in the looking-glass next to a crazy clump of ultramarine from nowhere.

Look at Matisse: his lush velvety still-lifes with anemones and simmering lemon; his airy hotel rooms looking out onto windswept palm avenues and streaks of sea; the witty angularity and purposeful unfinishedness of his tranquil young women. But above all look at Matisses series of bare drawings, his dogged explorations of one-and-the-same object his own starey-eyed face again and again, the tobacco jar filled with rough flowers again and again made with the brave fluid line that cuts straight back to the elegance of archaic Greece. So swift, simple and Mediterranean.

In our time of a morass of conflicting art efforts, this jumbled and would-be methodical show, with its handful of examples of marvellous things distilled from reality, is a lesson in defiance. More than ever it is a sorely needed example. Long live painting!

Bonnard, Matisse e il Mediterraneo. Until 4 Feb 2007. Complesso di Vittoriano, Via S. Pietro in Carcere (Fori Imperiali), tel. 066780664.

Mon-Thurs 09.30-19.30, Fri-Sat 09.30-23.30, Sun 09.30-20.30.