Rooney Mara: A street-fighting woman setting the screen on fire

The Girl with the Dragon Tattoo's Lisbeth Salander is the hottest Hollywood heroine for a generation

Fringe of society: Rooney Mara in 'The Girl with the Dragon Tattoo'

She mumbles, skulks and rarely makes eye contact. She eats only Happy Meals, wears only black and spends most of her life alone and online. She has no friends or family. She is, quite possibly, insane. And yet, Lisbeth Salander is the coolest heroine to emerge from Hollywood in decades.

If you want proof, look no further than the high street. Last week, H&M launched a clothing range inspired by the lead character of The Girl with the Dragon Tattoo, David Fincher's movie version of the bestselling crime novel. It's an idea that Salander herself would surely greet with a scowl and, if she could be bothered, a roll of her demonically kohled eyes, but you can see what the store was thinking. Here for the first time in too long is a truly original female character for women of all ages to idolise. Teenagers will love her sulky, screw-you, goth attitude; grown-ups will be wooed by her intriguing blend of strength and vulnerability.

Salander is the latest in a new wave of offbeat young heroines to hit the silver screen, following the foul-mouthed dynamo Hit Girl in Kick-Ass, and the superhuman wildchild, Hanna. In March, Katniss Everdeen (played by Jennifer Lawrence), the teenage hunter of the blockbusting Hunger Games franchise will also enter the fray. In fact, Salander first hit screens two years ago, played with sullen intensity by Noomi Rapace in the acclaimed Swedish version of the Millennium trilogy, but it is Rooney Mara's superstar-making turn that will bring the character to a wider audience. Not since the Alien films, led by Sigourney Weaver's Ellen Ripley, has there been a female-led cult series with so much potential for mass appeal – to men and women alike.

Like Ripley, though, Lisbeth's gender is the least interesting thing about her. Unlike the pneumatic Tomb Raider or PVC-clad Catwoman, she doesn't wear her womanhood like a badge. She is androgynous, bisexual and casually, incidentally promiscuous. Her look is distinctive – aggressive hair, a faceful of piercings, the famous tattoos – but there's also something strangely blank about it. Her monochrome clothes, bleached-out eyebrows and skeletal face make her almost invisible – a wraith kicking about in the shadows – which, of course, makes her all the better at the job in hand. She's interesting not for how she looks, or for who she kisses, but for what she does.

And what doesn't Salander do? She's a consummate "cracker" (computer hacker), a cerebral spy and a kick-ass fighter. She's fragile – dangerously so – but handles a gun and a motorbike with superhuman strength. So much so that James Bond himself (Daniel Craig, playing Mikael Blomkvist) is relegated to being her sidekick. "She's the one with the balls in this relationship," says Craig. "He's happy to watch while she beats someone up."

Like all the best Hollywood heroes, from Bond to Batman, Salander comes with an origins story of some complexity. It bristles behind her every move and monosyllabic utterance. We learn, drip by drip, of a troubled childhood. A ward of the state, brutalised by its bureaucrats, she struggles to control her sexual and violent impulses but has a fierce sense of good and evil. The scene in which she takes revenge on her sadistic guardian – wielding a sex toy and a tattoo gun, her eyes smeared in black glitter like an avenging angel – is one of the most unhinged in recent movie history. At the same time, she is tender, mutely falling for Blomkvist, even as she scorns him.

By the end of Fincher's magisterially paced film, it feels like we know less about her than we started. What finer attribute is there for a franchise lead? Lisbeth Salander leaves us wanting more – roll on the sequel.

'The Girl with the Dragon Tattoo' is released on 26 December