“This is where it all began for me,” Jason Bourne (Matt Damon) tells a former peer in the third act of The Bourne Ultimatum. “And this is where it ends.”

The producers say that The Bourne Ultimatum is the series finale and, in a sense, it surely is. After three films, Jason Bourne’s story is over. What began with an unconscious, anonymous figure floating in the Mediterranean with two bullet holes in his back ends with a single gunshot and another body of water. As for the rest of the film, it’s a gripping climax to the story of the amnesiac CIA “black-operations” agent who knows himself only as Jason Bourne.

As he did in The Bourne Supremacy, two-time Bourne director Paul Greengrass (United 93) seamlessly builds upon and extends the achievement of Doug Liman’s The Bourne Identity. The original film has grown in my esteem in the last five years, with its robust overarching premise, compulsively watchable set pieces and vivid location shooting. The first sequel, while lacking a key relationship that helped anchor the first film, went further in humanizing its hero while maintaining the same level of white-knuckle excitement.

The Bourne Ultimatum continues the series hallmarks of comparatively restrained realism, ferocious intensity, clever tactical thinking and an undercurrent of moral seriousness. Unlike the cartoon antics characterizing most of the James Bond franchise, the Bourne filmmakers know that keeping the action more or less human-scaled makes it more thrilling than pumping it up with over-the-top stunt sequences that could only exist in a movie fantasyland (even if a few scenes cross the line here and there).

They also know that a believable character with real emotions is more satisfying than a casually detached womanizer with interchangeable playmates.

The Bourne Ultimatum continues Bourne’s moral trajectory as he struggles not only to discover who he was, but also to decide who he wants to be.

The first film suggested an underlying decency in a man whose character was a mystery to himself. “I’m just trying to do the right thing here,” he told Marie and, in the end, we learned that it was resistance to doing the wrong thing that got Bourne dumped in the drink in the first place.

In the sequel, remarkably, Bourne led his black-ops pursuers on a breakneck chase as he delved into his past for information on an early hit assignment — not to compromise the Treadstone project or bring anyone down, as his pursuers feared, but to locate the next of kin to the people he murdered and apologize for his acts.

Now, in The Bourne Ultimatum, Bourne confronts the implications of his own involvement in Treadstone. How did he get to be a CIA hit man in the first place? What does that say about who he was before his bout with amnesia, and about who he truly is today? What was done to him to make him what he was, and what is his own moral responsibility?

There’s a revelation identical to a parallel discussion involving another amnesiac hero, the X-Men’s Wolverine, in X2. And if Ultimatum suggests that unprincipled assimilating tactics can mitigate an individual’s culpability for choices made under duress, it doesn’t exempt the assimilated from the obligations of conscience under the rubric of following orders. Bourne’s ultimate victory is not a tactical or martial one, but a moral one; his climactic confrontation with a former peer sent to kill him takes a dramatically different form from the brutal hand-to-hand combat that all previous such confrontations have taken.

The Bourne Ultimatum goes further into the ruthless expedience of the world of covert intelligence, in the process touching on such topical subjects as torture, extraordinary renditions and covert surveillance.

That’s a notable level of subtext in what continues to be one of the most action-packed series of all time, with one heart-pounding set piece following another almost without interruption in locations all over the world.

As usual, Bourne’s first weapon is his brain. He shows us how a man can become invisible by the simple act of tying his shoe, and how to hold a conversation of sorts with a reporter whose every line of connection to the world is being monitored. On the other hand, he isn’t infallible. There are setbacks and, more than once, a hostile asset kills someone Bourne is trying to protect. On one occasion the foe even outsmarts Bourne and maneuvers him into inadvertently assisting the hit.

As with previous installments, when there is violence, it’s grim, brutal and direct, without the dramatic flourishes and conceits of fisticuffs in popcorn movies like Die Hard. A harrowing battle with a very tough opponent in Morocco may leave you exhausted rather than exhilarated, which is at least arguably a more moral approach to violence than you get in the typical action movie.

With CIA heavies Brian Cox and Chris Cooper out of the picture, who’s sending the muscle after Bourne now? Meet the new boss, same as the old boss. A pair of ethically challenged administrators (David Strathairn and Scott Glenn) are out to essentially continue Treadstone’s charter under the code name Blackbriar and, once again, honest agent Pam Landy (Joan Allen) may be in a puddle too deep for her shoes.

Julia Stiles, who had one of the second film’s best-acted scenes, again makes a vivid impression as CIA agent Nikki Parsons. She’s got a bigger part this time around, and could almost fill the void left in the series by the death of Marie in the first act of The Bourne Supremacy, but the film doesn’t quite allow her to.

Despite some broad brushwork and a few lapses, the Bourne films are a rare achievement in today’s Hollywood, gripping action entertainment for thinking adults. The Bourne Ultimatum seals this achievement in grand style, completing a trilogy that stands as possibly the best-sustained such effort in the annals of Hollywood action moviemaking

Steven D. Greydanus is editor and

chief critic of DecentFilms.com.