The second part of any trilogy, however good it might be, inevitably has an unfinished quality—just think of “The Empire Strikes Back,” easily the best of all the “Star Wars” movies but one that ended with an unresolved cliff-hanger or two—or three. The rule applies even when the trilogy has been turned, for moneymaking purposes, into a quadrilogy, as has happened with “The Hunger Games.” This second installment, “Catching Fire,” ends with a twist similar to the big reveal of “Empire,” and with just as much unfinished business yet to come, now promised to be covered in not one but two further sequels.

“Fire” is also like “Empire” in that it’s an improvement on its predecessor. Not that “The Hunger Games” was bad, but it was merely adequate rather than exceptional, and not a little juvenile. This film, like its characters, is more mature, with deeper emotional undertones. That’s shown in the fact that once again fully half of the running time—some seventy-five minutes or more—is devoted to the run-up to the games, and when the nasty business pitting human against human does occur, it’s depicted even more than in the previous picture with a good deal of action but surprisingly little explicit violence; most of the deaths actually occur offscreen. Perhaps that’s just a factor of the resolve exhibited in “Hunger Games” to keep things within parameters suitable for viewing by an adolescent audience. But here it seems to be a prescription even more rigorously followed.

“Catching Fire” takes up where “Games” left off, with Katniss Everdeen (Jennifer Lawrence, again outstanding) and Peeta Mellark (Josh Hutcherson), having won the games, being prepared for their victory tour of the provinces as putative young lovers under the watchful eyes of furious, vengeful President Snow (Donald Sutherland), who’s determined to punish the less-than-docile heroine for outwitting him. His solution, suggested by new game-master Plutarch Heavensbee (Philip Seymour Hoffman), is to alter the 75th anniversary of the event by pitting former winners against each other. That means that Katniss and Peeta will have to fight to survive again, along with a group that includes many formidable foes. And the entire celebration is happening against a backdrop of simmering rebellion exacerbated by Katniss’ obvious disaffection, which has led to her real love Gale (Liam Hemsworth) being brutally treated by the vicious new governor of District 12 for his resistance.

Most of the other so-called tributes are peripheral characters, but some stand out as allies of the central couple, even if their loyalty must be considered doubtful. They include Finnick Odair (Sam Claflin), a raffish hunk, and his mute elderly mentor Mags (Lynn Cohen); cynical, tart-tongued Johanna Mason (Jena Malone); and spacey couple Wiress and Beetee, nicknamed Nuts and Volts (Amanda Plummer and Jeffrey Wright). They band together with Katniss and Peeta to try to survive not only their opponent but the potentially fatal complexities of the game Plutarch has fiendishly constructed, which include poisonous gas, electrical force-fields and a herd of bloodthirsty orangutans (which look unhappily as though they’d been carried over from their scenes in “After Earth”). It wouldn’t be fair to reveal much about how the contest proceeds, though it will come as no surprise that while some players fall, the major ones survive to fight another day, even if some are left in peril (yet another way in which the script recalls “The Empire Strikes Back”). There are two more movies in the franchise pipeline, after all.

Though Katniss, Peeta and Snow are the major carryovers—and they’re all well played, with Lawrence capturing the full range of Everdeen’s emotions, Hutcherson making a quietly supportive partner, and Sutherland positively oozing menace—“Catching Fire” returns plenty of other characters from the first film in the series. In addition to Gale, there are the heroic couple’s trainer Haymitch Abernathy (Woody Harrelson) and promoter Effie Trinket (Elizabeth Banks), as well as Katniss’ stylist Cinna (Lenny Kravitz) and the games’ frenetic announcer Caesar Flickerman (Stanley Tucci), to mention only the most prominent of them. All equal, if not surpass, their work in the previous picture, and Hemsworth again makes a stalwartly macho lover-in-waiting. Among the newcomers Hoffman stands out as the devious Heavensbee, but Cliflin, Malone, Wright and Plummer all fill out their characters nicely. The lesser roles are ably taken, too.

The look is less than important in these films than in other effects spectaculars, since the characters mean more here. But “Catching Fire” is technically very fine. Though Francis Lawrence’s direction isn’t so much inspired as workmanlike, he, cinematographer Jo Willems and editor Alan Edward Bell have worked together to make it visually crisp, narratively clear and well-paced; it’s a distinct improvement over Lawrence’s previous films, and actually feels shorter than its 146-minute running-time. The production design by Philip Messina, art direction by John Collins, Robert Fechtman and Adam Davis, set decoration by Larry Dias and costume design by Trish Summerville are all significant positives. Once again, though, James Newton Howard’s score sounds generic.

The original “Hunger Games” didn’t really catch fire, but—as the subtitle promises—this sequel does. Though the inconclusive ending necessarily leaves you hanging, it also leaves you wanting more, which is the most important thing a “part two” can accomplish. Readers of the books should be more than satisfied, and non-devotees will find this a smoother, more affecting ride than its predecessor as well.