To call David Fincher’s “The Girl with The Dragon Tattoo” a remake of the excellent 2009 Swedish thriller wouldn’t be fair. Yes, it too is based on the runaway bestseller by the late Stieg Larsson, but Fincher has taken this material and, with the help of ace screenwriter Steve Zaillian, made it his own. His version proves to be one which is neither better nor worse than the original, but one which effectively stands on its own two feet to where any comparisons are not really necessary.

Daniel Craig takes on the role of Millennium Magazine writer Mikael Blomkvist who, at the movie’s start, has lost a libel case against the wealthy but corrupt businessman Hans-Erik Wennerström, a defeat which will seriously deplete his savings account. To escape the prying eyes of the press, he accepts an invitation from retired CEO Henrik Vanger (Christopher Plummer) to investigate the mysterious disappearance of his great-niece Harriet. Vanger believes she may have been murdered by a member of his family, one which proves to be far more dysfunctional than any you may know.

Fincher’s film takes its time in establishing the characters of Blomkvist and Salander, who is played here by Rooney Mara. In fact, they don’t meet face to face until an hour into the movie. While studio executives were probably begging to see these two come together a lot sooner, it gives these actors time to establish their characters to where we feel like we understand them and are eager to see each work with one another.

Stepping outside of the James Bond franchise, Craig is terrific in conveying Blomkvist’s single-mindedness in finding answers which need to be uncovered. This is not a heroic character taking out the bad guys with relative ease, but one who is dedicated to finding out the truth and soon comes to realize just how much danger he is in. But as frightened as he is, Blomkvist is in no position to just give up and go home.

As for Mara, her performance as Lisbeth Salander is nothing short of a revelation. She must have given one hell of an audition for Fincher because very little in her resume, certainly not the bland “Nightmare on Elm Street” remake, could have prepared us for how good she is here. That is, except for her performance as Max Zuckerberg’s girlfriend who dumps him without remorse at the beginning of “The Social Network.”

Having watched Noomi Rapace inhabit this character previously, it was hard to think of another actress who could be anywhere as good in playing Lisbeth Salander. Mara, however, is more than up for the challenge, and her commitment in portraying this understandably anti-social character is utterly complete. I kept trying to find traces of Mara in this film, but I came out of it feeling like I never saw her. Instead, I felt like was watching Lisbeth Salander and no one else. Now this is a performance worthy of awards consideration!

Not to take away from Rapace’s star-making performance, but Mara has the advantage here of dealing with this character’s complexities which were not as deeply explored in the 2009 film. While Mara puts up a tough exterior, she simultaneously allows you to see those cracks of vulnerability hiding just beneath the surface. You fear for Lisbeth even though you know she eventually will kick ass.

There are many other great performances to be found here, and the actors have the fortune of playing characters which are given more depth in this version. Plummer has had quite the year with this and “Beginners,” and he gives Henrik a biting sense of humor which has aided him in dealing with the emotionally sordid history of his family. Robin Wright pulls off a surprisingly confident Swedish accent as Blomkvist’s co-worker and lover Erika Berger. Steven Berkoff of “Beverly Hills Cop” and “A Clockwork Orange” fame is a strong presence as Henrik’s lawyer Dirch Frode, Stellan Skarsgård remains one of the most reliable actors in movies with his performance as Martin Vanger, and Joely Richardson is fantastic as Anita.

Director of Photography Jeff Cronenweth does a superb job of capturing the frozen landscapes of Sweden to where you get frigid just looking at the screen. The scene where Blomkvist desperately tries to warm up the cottage Vagner has provided for him pushes this point across than it would ever need to. I haven’t shivered this much since after I finished swimming the 2011 Los Angeles Marathon.

Fincher’s movie also has a mesmerizing score from Trent Reznor and Atticus Ross, both whom won the Best Original Score Oscar for their work on “The Social Network.” They give the story and its characters a sonic soundscape unlike the typical orchestral score, and it brilliantly captures the growing emotions which get stronger and stronger as the movie reaches its brutal climax.

Speaking of brutal, Fincher never sugarcoats this story or makes it easy to digest down to a PG-13 rating. In retrospect, I’m not sure there was a way he could as it deals with serial killers and features a vicious rape perpetrated on the main character. As with the majority of his movies, Fincher’s vision of the world is a dark one where the characters can be as cold as the snowy weather, but his vision also remains one of the most powerful in today’s cinematic world.

When it comes to comparing the 2009 and 2011 movies, this one has an upper hand in that it’s far more cinematic. The original Swedish film was actually a television miniseries which got shortened when released theatrically. That one remains a great thriller worth watching, but David Fincher’s version of “The Girl with The Dragon Tattoo” threatens to be more compelling as it builds on the original without taking away from it. I have yet to see him make a truly bad motion picture, and yes, that includes “Alien 3.”

* * * * out of * * * *