"If you re-make a good film," says Michael Caine, starring with Jude Law in Kenneth Branagh's Sleuth, "you're on a hiding to nothing." He is almost always right. But Branagh's version of the Anthony Schaffer play, filmed in 1970 with Laurence Olivier, and presented in competition at Venice, is not your usual re-make. It has a new screenplay from Harold Pinter which is entirely different in emphasis.

This time around, Caine plays the famous writer of thrillers who takes his revenge on the man who has run off with his wife and Jude Law is in the part Caine originally played as the part-time actor and hairdresser who has cuckolded him. And though there is still the famous battle of wits between the two, the emphasis is both bleaker and blacker.

The writer is more like a real psychopathic killer taking his cue from the twisted plots of his own books than just a bitter games-playing eccentric. He lives not in an old country house but a vastly expensive contemporary mansion of steel, glass and concrete, the electronic controls of which he manipulates as shrewdly as he does the younger man who has so cruelly betrayed him.

Caine, given plenty of close-ups by Branagh, gives as complete a performance as Olivier did in the old film, while Law acts against him as the weaker actor with a sure touch, except when he has to impersonate the detective arriving to accuse the writer of attempted murder. That scene is the weakest in the film. Otherwise Pinter, allowing for plenty of spiked humour particularly in the opening sequences, ratchets up the tension in his inimitable spare style.

The result is still highly theatrical rather than truly cinematic, played out like a deadly game of ping pong between two men who are vulnerable in different ways.

But if it would look more comfortable on the stage, at least Branagh's 85-minute film is wise enough to keep things short and sharp.