JASON BOURNE looks sore. His face is crinkled, lined with dirt, and his eyes dull with tiredness.

He is injured. He has just survived a Moscow car chase in The Bourne Supremacy and now they want him to do a third film, The Bourne Ultimatum.

Ouch. Not even the weekend off.

Trailing blood, he breaks into a pharmacy to get supplies. Soon, the world's most deadly CIA assassin with memory loss is patched up and ready to go a third time. He doesn't look pleased. One presumes the unspoken ultimatum of the title was a warning to the producers: two weeks off after this, or I'll kill you and your families.

Jason Bourne, the only spy who can notch up more carbon emissions than James Bond (he would thrash him in a fight too) is surprisingly healthier than ever.

And The Bourne Ultimatum, the second Bourne film helmed by British director Paul Greengrass, is a topper: it's a frenetic, nervy thriller that is impossible to pin down. The only person who seems to know where it is going is Bourne himself, but he seems to be hardwired with a Global Positioning System; he is always one move ahead of everybody else.

Greengrass, the English filmmaker who used to make docu-dramas, is now proving himself one of the most talented directors in Hollywood.

Beginning his career on TV's World in Action was more savvy than we had thought. His style looks like documentary, but is a sinuous, simulated reality. In United 93 he took a foregone conclusion (the crash of the fourth 9/11 passenger jet) and by the end had us shouting out of our seats in support for the doomed passengers.

In The Bourne Ultimatum, this approach makes you feel you are about two feet away from Matt Damon's Bourne . . . a man who thinks and moves so fast, you feel the fizz of his electricity on your skin. Greengrass's intense realism corrals this tension: as the end credits rolled, there was a twisted lump of styrofoam in my sweaty palm that once held coffee. For a threequel, I have to concede this exceeded my expectations, and then some.

(And you know my antipathy to threequels. ) Matt Damon clearly has a taste for the political with recent choices including Syriana and The Good Shepherd. In that film, the CIA operated with measured intelligence . . . lots of cloak, a little dagger. But this post 9/11 crew is shaped like an enormous hunting knife. It's led by David Strathairn's Noah Vosen, a deputy director in charge of Operation Blackbriar . . . a murderous black ops unit with no red tape. Their aggression is apparent when Vosen orders a hit on Bourne and Guardian newspaper journalist Simon Ross (Paddy Considine) in the middle of London's Waterloo station.

Ross has sniffed out Bourne's story but is in too deep. The result is spectacularly messy. "Decisions made in real time are never perfect, " Vosen tells Pamela Landy (Joan Allen), a deputy director he ignores most of the time.

The story continues Bourne's quest for his real identity and the CIA comes off very badly indeed.

Hazy memories begin to resurface of something sinister during training. We are whisked through Moscow, Paris, London, Madrid, Tangier and New York, while Bourne takes CIA agent Nicky Parsons (Julia Stiles) along for the ride. (You can forget about romance . . . Bourne is too busy improvising his way out of trouble. ) Back at CIA HQ, it is Landy who intuits that Bourne wants to come in. And she suspects the CIA bosses are hiding something, particularly when Vosen wants to whack Parsons too. "You start down this path, where does it end?" she exclaims at the ruthless brutality.

"It ends when we have won, " retorts Vosen. Bourne knows far too much about the CIA's dirty laundry.

The film's language makes the traditional Hollywood thriller . . .with its over-reliance on special effects and grand staging . . . look redundant. Many scenes look filmed by accident, or with an intimate camera. Footage is assembled from CCTV, hand-held cameras, or sometimes we observe with the CIA, watching on their monitors. Edited together, it creates a stew of paranoia. Add to this the long sequences where Greengrass has assembled about four tiers of chase . . . the CIA is after Bourne, he is tailing an assassin who is pouncing on Parsons, while the Moroccan police follow Bourne's contrails . . . and you have a great cat and mouse chase movie.

Even if you were to subtract the political analogies (let's see: that America needs to purge itself of administrative rot? That it needs more feminine intuition? ), it has oodles of intelligence in just the way it sustains this energy. But please Matt Damon, say no to number four.