Here’s a quick list of some of the good stuff the films share. Both films are based on Robert Ludlum novels. Behind the screen, Tony Gilroy returns as screenwriter. Cinematographer Oliver Wood and composer John Powell are back. On screen, in supporting roles, Brian Cox, Julia Stiles and, all too briefly, Franka Potente are back.

Back as the title character Jason Bourne is Matt Damon. Again, he gives an assured, tempered performance as the American black ops assassin who still suffers from substantial memory loss. He makes us care about his future and his past.

In The Bourne Identity, Jason Bourne was suffering from complete memory loss, at least in terms of his identity. He could easily remember how to do all things spy and assassin like, but even when told his name he had no idea who he was or what he had been doing. He was targeted for assassination when his intelligence community colleagues decided he suffered a mental breakdown and had become a loose cannon and a liability.

But Jason was the best agent this super secret project had, and he eliminated all who tried to kill him. At the end of The Bourne Identity, he warned his former employers to leave him alone. He and Marie, the girl who helped him elude so many killers, were going off into the world to disappear and live quietly. He threatened that if they came after him, he would return the favor and come after them.

The Bourne Supremacy begins with Jason and Marie living on the beach in India. It is a couple of years later, but Jason is still plagued by nightmares he cannot interpret. He is always on edge, scoping out every situation to make sure no one is stalking them. He’s more than a little paranoid, but then again, there have been many people out to get him.

And when it becomes convenient, some of his ex-colleagues frame him to cover their trail. They plant his fingerprint at the scene of a couple of murders and the theft of millions of dollars and some documents. They also send a hitman after him.

So Jason Bourne is on the run again, and he comes after his former employers, just as he promised. Once The Bourne Supremacy hits the road, the soothing familiarity of the action genre heats up.

Like The Bourne Identity, the new film makes exhilarating use of foreign locations. India, Naples, Berlin and Moscow are all photographed to look great and accentuate their foreign-ness. They look great but also mysterious and dangerous.

One of the most satisfying elements of both Bourne films is that they do not rely on phony tricks. No jumping from fast-moving trains to other fast-moving vehicles or other acts defying the laws of physics like some action franchises. Jason navigates every difficulty with brains and skill, putting his deadly training to satisfying use. He works with tools, techniques and tricks that are humanly possible. (It is a little goofy that Jason never tries to conceal his identity. We understand that he is tough and fearless, but he does have an objective and lots of people out to get him. Would sunglasses or a hat be completely out of order?)

But mostly, Jason uses his believable abilities against equally believable foes who are driven by very plausible motivations. Oil, money, power, reputation, mistakes and bad judgment are driving the behavior of the bad guys. The bad guys are corrupt Russian politicians and inept CIA career bureaucrats. Not too much of a stretch.

Instead of feeling too familiar or predictable, these stock elements are presented with enough semblance of reality and forward motion that the effect is very satisfying. I’m not a big fan of car chases, but the final pursuit through the streets of Moscow is heart-pounding because the use of realistic stunts has been sustained throughout the film.

What I missed in Supremacy is, first, the presence of interesting women. Identity belonged almost as much to Marie as it did to Jason. Potente, the star of the dazzling Run Lola Run, had more experience in Identity as an action hero than Matt Damon. Marie disappears way too early in Supremacy. It is a beautifully photographed, if inevitable departure. It is the most emotional scene in either film, and, though Jason clings tightly to the good she does for him, a little of the fun leaves the movie when she departs.

To make up for her loss, Julia Stiles gets a little more screen time. Stiles is a fine actress, and she does a good job in this movie, but she is just a cherubic-faced, girl-next-door American, no matter how sophisticated her hair looks.

Joan Allen has also been added to the cast as a senior CIA operative. She’s in charge of the operation that Jason’s fingerprint suggests he sabotaged. Allen is also a fine actress, but she is playing a character that doesn’t really rise above cliché. She’s the embattled woman in a man’s world. She has played many characters where pursing her lips and looking stern and tough are very important, and that’s mostly what she does here.

The other change that is not for the better from Identity to Supremacy is the change in director. Identity was directed by Doug Liman, who serves as an executive producer for the new film. Supremacy is directed by Paul Greengrass. The only film by Greengrass I have seen is Bloody Sunday, a film about the 1972 riots between British soldiers and Irish patriots in Derry, Northern Ireland, a film with a lot of virtues but one big problem that he visits on Supremacy.

Supremacy is constantly on the move, as was Identity, but the camera rarely stops rattling in Supremacy, and it is annoying and distracting. It was unnecessary in Identity, and it is unnecessary now. The story is strong enough. We don’t need constant cuts and constant motion to be interested. We care enough about Jason and his inner and outer struggles and don’t need editing and camera jiggling to convince us that Jason is in jeopardy. Even in the chase scene the camera doesn’t trust what is on screen. This isn’t the sequel to Charlie’s Angels. Trust the material!

Jason learns a little more about himself and his former life in Supremacy, but there is still lots he and we don’t know. And there is another novel. And sequels don’t have to stop just because there is no novel to start with.

The Bourne Supremacy ends with the same great song, “Extreme Ways,” playing as the movie fades to black. Moby sings, “I would stand in line for this. There’s always room in life for this.” I won’t stand in line, but I’ll look forward to the next installment.