When you dare open your film with a biblical quote about revenge, as “True Grit” does, you better deliver a story about revenge, and it better be epic.

Rest assured, writing/directing siblings Joel and Ethan Coen (“No Country for Old Men”) have done that with their latest foray into the sinister side of the American West. Although a remake of the ever-beloved 1969 classic of the same name starring John Wayne, this take on the iconic Western is very much its own animal.

Even if that animal is a dead bear draped atop a burly stranger itching to trade a corpse. This is, after all, Coen brothers territory — an area paved wildly with idiosyncrasy.

Opening today, the film begins with the dead body of a man murdered, the sparse narration tells us, by a wily thief named Tom Chaney (Josh Brolin, “Wall Street: Money Never Sleeps”). Acting on her own, Mattie Ross, the deceased’s headstrong young daughter (relative newcomer Hailee Steinfeld), comes to Arkansas to retrieve his body and settle some business.

That business, belonging to no one but her, is one of vengeance: hunting down Chaney in Indian Territory and shooting him dead. Such an act would prove difficult, if not impossible, for a teen with pigtails, so she bargains her father’s few possessions in exchange for cash she dangles in front of the nose of U.S. Marshal Rooster Cogburn (Jeff Bridges, “TRON: Legacy”).

Disgraced and one-eyed, Cogburn isn’t interested in anything that doesn’t inebriate. Spur-booted Texas Ranger LaBoeuf (Matt Damon, “Green Zone”) is, but to bring him to justice, thus denying Mattie her revenge. Before long, the three team up, somewhat unwittingly, and set out on horseback to find Chaney.

Their adventure slowly spellbinds — like “No Country for Old Men,” it’s paced purposefully to wring suspense and drown viewers in its near-alien landscape of sagebrush and snow, showcased in beautiful, stunning images by the Coens’ frequent cinematographer, Roger Deakins.

This take on the iconic Western is very much its own animal.

How strange for Bridges to jump into another role of a grizzly alcoholic seeking redemption so soon after last year’s Oscar-winning turn in “Crazy Heart.” As if he realized as much (and probably did), he lacquers on the vocal affectations of Billy Bob Thornton in “Sling Blade” so at least he’ll sound different. The unkempt look, however, is intact.

No matter, because Cogburn remains a compelling character, but the picture is stolen outright — if not immediately — by Steinfeld. The unknown actress, newly 14, previously had little on her résumé beyond appearances on unremarkable sitcoms. She possesses such confidence and maturity that she’s likely to cap her rise with an Academy Award nomination. Not only is she that good, she’s that great.

Remaking a film is always a dicey proposition — just ask the Coens, who tanked with 2004’s “The Ladykillers” — but this one bears so much of their trademark stamp, while remaining faithful to Charles Portis’ 1968 novel, that it’s worthy of wearing the eye patch.

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