Well, that's that. I clearly have to watch all of Tetsuya Nakashima's movies, then.

He made Memories of Matsuko, which will never stop gobsmacking me. He made Confessions, about which I hear lots of good (but dark) things and which was Japan's submission for that year's Best Foreign Language Film Oscar. Before those, though, he made this and for it won the Best Director award at the 2005 Yokohama Film Festival.

Fortunately it has nothing to do with suicide or World War Two. Ignore that "kamikaze" in the English-language title, since the original is called Shimotsuma Story, after the city it's set in. Instead it's a heavily stylised comedy based on a light novel, about two anti-social characters who don't fit in and are determined to live their own way. These are:

1. Momoko (Kyoko Fukada)

...is a Dedicated Follower of (Lolita) Fashion. Her favourite historical period is France in the 18th century, because that's when they invented Rococo style. She wears frills on her frills. She's dyed her hair caramel-colour. She buys her clothes at Baby, The Stars Shine Bright and is legendary there, to the extent that one day the designer comes out to thank her personally. She dresses like a wedding cake and she comes across as a freak... which is exactly what she is. She thinks it's best to be alone, that emotional connection to others is pointless and that it's perfectly okay to lie, cheat and rip off her family (of criminally inclined freaks) for clothes money.

I liked her. You'd expect someone like that to be miserable, but she's actually chirpy and optimistic. She's a monster of selfishness, but she admits this and has no filters whatsoever on what she says to people. She doesn't think it's wrong, you see. Happiness is what matters. We should all try to be happy. Just don't lend her any money, because you won't get it back and she'll say so to your face.

She's the film's protagonist and narrator and it's amazing to see the world through these pink-frilled, happy but deeply warped eyes. You know all those little things that people do to get on better with others? Fukada doesn't do them.

2. Ichigo/ko (Anna Tsuchiya)

...is a biker girl. She talks like a gangster and she often punches or head-butts Fukada. She's checked out of regular society, she's nearly illiterate and her head is full of people who live by violence. However at the same time, paradoxically, she's got a strong code of honour and she's far more of a straight shooter than Fukada. If you lend her money, for instance, you'll get it back even if it costs Tsuchiya a pint of her own blood.

These two people are not natural friends. Fukada in particular doesn't care two hoots about this thug and doesn't even pretend to listen when Tsuchiya's telling her a story. When told that they're friends, Fukada's response is to go to a vegetable stall, buy a cabbage and give it to Tsuchiya that this is her new (green, spherical) friend. She then runs off, saying, "Goodbye, legendary idiot."

Tsuchiya either doesn't notice or doesn't care. If Tsuchiya decides you're going to go somewhere with her, it's hard to get the word "no" through to her.

This is great in itself. The characters on their own are worth watching, going from surreal comedy to peculiar and deeply personal scenes of emotion. It's bonkers, but moving. And also bonkers. Seeing Fukada overcome the massive obstacle of her own personality and charge off to rescue Tsuchiya... well, it's like watching an alien from another planet. Then there's the question of their childhood selves, whom we meet in flashback scenes and then meet again at the end. There's a coda, in which our heroines have fairly routine happy endings and then ditch them because they're not their style. Formulaic happy endings get binned. Instead we have a far more meaningful one as these girls defiantly go on doing their own thing, as they've been doing from the beginning and will keep on doing until the day they die. It's glorious, albeit in a slightly self-destructive way. It'll make you want to stand up and cheer.

Anyway, this has throwaway magical realism as both girls unknowingly pass their childhood selves in the street. The children seem to approve.

That's half the film. The other half is Tetsuya Nakashima's direction, which is wacky. He has Fukada talking directly to us. He has a brief anime segment. The first ten minutes or so are particularly frenetic, including gags like the traditional "camera zooms in on a map" shot ending on a man's head... only for him to look up the camera and punch it, saying, "Get out of my face!" It's a silly, light-hearted style that soon settles down, but it gives strange, whimsical energy to the film and I loved it to bits.

You can tell it's from the director of Memories of Matsuko, although I'm sure his films aren't all like this. They couldn't be.

Meanwhile the acting's award-winning. Both leads won film awards for what they did here and quite rightly. Fukada completely inhabits her bizarre role and makes a triumph of it. She tends to get overshadowed by Tsuchiya in discussion of the two performances, but hers is actually a far more difficult role and it's her who carries the film. I thought she was outstanding. Meanwhile Tsuchiya is an actress, model and singer who only acts from time to time, but this is both her debut and her best-known role and she changed it completely from the one in the original book. The character you see here is apparently drawn in large part from Tsuchiya's own life. It's one hell of a beginning to one's acting career and she could easily have taken far more work than she's done so far, although that's not to say at all that she's done nothing.

Mind you, it's not a two-woman show. For instance, I defy anyone not to adore Yoshinori Okada as the camp designer whom Fukuda calls "God". Could he be more perfect? I think not.

It's a freaky film. It's heartwarming, because it travels so far into bizarre, anti-social and openly abusive to get there. I always used to get it confused with the following year's Nana, by the way, which is similarly about two Japanese female friends (one punk, one not) and became a bigger franchise (21 manga volumes, two live-action films, 47 anime episodes), but Kamikaze Girls is way more extreme. It's also quite well-known, far more so than most of the Japanese films I watch. I've had it on my radar for years. There's a reason for that; it's often the good things that get well known. I wasn't joking about being about to hunt down all of Tetsuya Nakashima's movies.