“The Bourne Legacy” looks bad on paper. The fourth instalment of the hugely successful franchise starring Matt Damon as the memory-depleted assassin Jason Bourne does not star Damon, doesn’t feature his character and does not arrive by way of director Paul Greengrass, whose jagged, shaky-camera visual technique became as identifiable a marker of the series as Damon’s appealingly vulnerable hero.But - surprise, surprise - “The Bourne Legacy” looks surprisingly good on-screen, precisely because it’s so good on paper. Written and directed by Tony Gilroy, who penned all three Jason Bourne movies, “The Bourne Legacy” achieves its first order of business with intelligence and imaginative dexterity, building on the preexisting story, expanding its human capital and geography, and leaving plenty of white space for Jason to jump back in if Damon and Greengrass ever decide to return.And Gilroy has fulfilled the movie’s second requirement with similar success, casting Jeremy Renner in a leading role that asks him to carry “The Bourne Legacy” while easily co-existing with the titular ghost that haunts the franchise.The only thing missing is that peripatetic camera - which will be good news for viewers who needed Sea-Bands before watching the Greengrass oeuvre. Gilroy, who made a smashing directorial debut with “Michael Clayton” and a twisty romantic caper with “Duplicity”, hews unapologetically to the classical cinematic style, with a minimum of self-conscious flourishes or attention-getting edits. “The Bourne Legacy”, which he wrote with his brother Dan, unfolds with disarming straightforwardness - a distinct advantage for a story that requires that spectators lean in and pay attention rather than zone out and take it all in.Gilroy’s most brilliant stroke of insight with “The Bourne Legacy” was to set it within the reality of “The Bourne Ultimatum,” the most recent of the movies that ended, if you recall, with Our Man dangerously at large in Manhattan.“The Bourne Legacy” opens thousands of miles away in Alaska, where another agent, Aaron Cross (Renner), is finishing a grueling training regimen, tramping over snowy wilderness, taking mysterious green and blue pills and going mano-a-mano with a wolf that would have given Liam Neeson pause in “The Grey”.How are Jason and Aaron related? Why are shadowy figures within the CIA, US military and private security contractors so worried about him? What does an attractive genetic scientist played by Rachel Weisz have to do with it? And, finally, can Renner look as cool leading an epic motorcycle chase through Manila as Damon did leading an epic car chase through Moscow in “The Bourne Supremacy”?The answer is yes, even if the motorbike sequence goes on far too long. The acrobatics that Renner engages in along the way - like a nifty two-wheel slide down a stone banister - are preceded by just a handful of suspend-all-disbelief moments, including a similarly spectacular slide down a slot canyon in a back alley and an out-of-left-field rescue at a pivotal character’s suburban home.But for the most part, “The Bourne Legacy” takes place in an impressively recognisable world, where science, hands-free geopolitics and the modern security state intersect to create human warriors who behave like the human equivalent of drones (without those pesky sentient emotions).It’s that world and its ruthless thought-leaders (here portrayed in terrific performances by Edward Norton, Stacy Keach and Dennis Boutsikaris) that Aaron must navigate - with his memory intact, but driven by just as dramatic an inner need.At least that’s clearly what Gilroy intended; unfortunately, Aaron Cross’ personal struggle isn’t nearly as narratively propulsive as Jason Bourne’s amnaesia. Still, Renner makes for an intense, highly watchable franchise-anchor-in-the-making, his character a combination of high-IQ savant and MacGyver-like Mr Fix-It, who can whip up a clever anti-detection device with duct tape and an aluminum pie plate. Renner’s enormous appeal has always resided in his ability to project star power (witness his Oscar-nominated work in “The Hurt Locker”) as well as un-showy, everyman believability (witness his Oscar-nominated work in “The Town”). Both work to his advantage here, although it would be nice for those glints of spontaneous humor to get more play in succeeding productions.Whether there will be more productions depends on “Bourne” fans’ willingness to let go of Jason and throw down with Aaron, at least for the time being. With “The Bourne Legacy,” Gilroy has brought characteristic taste and skill to a nearly impossible task: embracing the past without completely erasing it, thereby creating an invitingly complicated and open-ended future.The Bourne Legacy (PG-13) is showing at the Speciality Cinema