Matt Damon has been knocking around movies for nearly 20 years now, and he’s been a star for at least a decade, since the overrated Good Will Hunting. For much of that time, though, he’s suffered from a sort of Leonardo DiCaprio-it is — he seemed like a callow, unformed boy playing at being an adult. When he was effective in earlier years, it was in roles that exploited this, like his fine title turn in The Talented Mr. Ripley.

Also like DiCaprio, in more recent years he’s managed to shake this boy-in-oversized-shoes quality. His role (opposite DiCaprio) in Scorcese’s The Departed has helped with this, but it’s his startling command as Robert Ludlum’s existential spy hero Jason Bourne in The Bourne Identity (2002) and The Bourne Supremacy (2003) that’s really made him grow into a tough guy.

Seeing Damon in action as Bourne on a big-screen TV, one of the characters in The 40-Year-Old Virgin sums up the shift in perception when he remarks “Y’know, I always thought that Matt Damon was like a Streisand, but I think he’s rockin’ the [house] in this one!”

He rocks it again in The Bourne Ultimatum, the third entry in the successful franchise. He doesn’t have all that many lines here—the expository duties are handled by such pros as Joan Allen, David Strathairn, Albert Finney and Scott Glenn.

Damon’s Bourne, meanwhile, spends most of his footage stalking through streets and alleys and back hallways and over rooftops, dodging relentless CIA surveillance and cold-eyed assassins across London, Madrid, Tangier and New York, as he continues his quest to find out who he is and who turned him into a programmed amnesiac killer.

You can see Bourne’s haunted unhappiness on Damon’s pug-nosed pan, which is cragging up a little—from cute to truly handsome—as his 30s progress. But the actor doesn’t milk it; he has a becoming reticence here, almost as if he were deliberately angling his face away from the camera.

As solid a star presence as Damon is, though, The Bourne Ultimatum draws its energy from the headlong direction of Paul Greengrass, the Englishman who also helmed Supremacy and who made such a pulse-pounding experience of United 93.

Greengrass likes to work with rapid-fire cuts and a lot of shaky hand-held camera, but he never gets so caught up in this razzle-dazzle that we lose track of what’s going on. Although Julia Stiles is back as Bourne’s ally, the two aren’t allowed a love scene—the movie never really slows down for more than a quick breath between a series of set-piece action scenes.

An early one, through Waterloo Station in London, is particularly gripping.

On the whole, this is the best action picture I’ve seen in a long time — at least since Quentin Tarantino’s Death Proof, which didn’t get going until its last 20 minutes.

The Bourne film goes on, perhaps, a few minutes too long, and in the New York scenes toward the end it grows a little cheeky in the James Bond manner, with Bourne engaging in death-defying derring-do that made me strain to keep my disbelief suspended.

Ultimatum also persists in a certain silly but touching naiveté: The plot hinges, in part, on the premise that if the public were to learn, through the media, that our intelligence community was engaging in torture and murder, there’d be prompt congressional hearings and indictments.

It’s a charmingly dated notion, like the belief that true love conquers all.