When news broke that a sequel of sorts was being made to Abel Ferrara's startling 1992 tale of lost humanity, Bad Lieutenant, the initial buzz was not positive. Most critics expected an ill-conceived, straight-to-DVD effort that would be seen only by the foolish few who failed to spot that the original creative team was not involved this time around.But all that was before Werner Herzog became involved.

The German filmmaker is, after all, about as far from a hack as it is possible to be in modern cinema. This is a man who has defied expectations to bring his highly personal and idiosyncratic visions to the big screen time after time, telling stories which no other film-maker would have had the nerve or ambition to touch, and telling them in ways which no other director would have considered.

Films such as 1972's Aguirre, the Wrath of God, the tale of a band of conquistadores trying to find the lost city of El Dorado; 1982's Fitzcarraldo, in which the title character pulls a steamer ship over a Peruvian mountain to secure an untapped rubber plantation. Both are classic tales of insane overreachers. Herzog's documentaries Grizzly Man and Little Dieter Needs to Fly, meanwhile, centre on highly unusual protagonists, men whose dangerous charisma and determination to achieve their goals may have consequences for those who are drawn to them.

A similar spirit runs through Herzog's Bad Lieutenant, which the filmmaker only accepted after screenwriter Billy Finkelstein made him a solemn oath that the film was not a remake. (The US release of the film was given an expanded title: The Bad Lieutenant: Port of Call – New Orleans.)

"It does not bespeak great wisdom to call the film The Bad Lieutenant," Herzog says of the matter. "But the film industry has its own rationale, which in this case was the speculation of starting some sort of a franchise. I have no problem with this.

"What the producers accepted was my suggestion to make the title more specific – Port of Call, New Orleans – and now the film's title combines both elements. Originally, the screenplay was written with New York as a backdrop, and again the rationale of the producers set in by moving it to New Orleans, since shooting there would mean a substantial tax benefit. It was a move I immediately welcomed. "In New Orleans it was not only the levees that breeched, but it was civility itself: there was a highly visible breakdown of good citizenship and order. Looting was rampant."

Herzog set about creating "a new form of film noir" in which "evil was not just the most natural occurrence. It was the bliss of evil which pervades everything in this film". His partner in crime was Nicolas Cage, who agreed to take the central role of Terrence McDonagh, a lieutenant with the New Orleans police department who becomes addicted to painkillers, illegal drugs and abuse of power in the wake of an accident that leaves him with crippling back pain.

McDonagh is a man living on survival instincts alone, who long ago abandoned all thought of foresight or forward planning. He needs drugs, for himself and his prostitute girlfriend (Eva Mendes), so he raids the evidence room for narcotics, or pounces with badge and gun on revellers as they emerge from nightclubs.

At first, he continues to defy logic and serve as an effective investigator of the murder of a local drug dealer and his family. But when he needs the likely killers' help to secure fast cash to pay off a gang of ruthless gangsters, the search for justice is put quietly to one side.

Cage plays the role with the desperate but fearless air of a man who has long since lost the grace of God. His McDonagh is a larger than life creation with an insouciant swagger and harebrained confidence, yet this never feels like a performance of shabby scenery-chewing. Herzog, for his part, always holds the movie just the right side of farce. "Nicolas Cage followed me ... with blind faith," says the director. "It became instantly clear that we would do this film together, or neither one of us would do it. There was an urge in both of us to join forces."

The eminent critic Roger Ebert named Bad Lieutenant one of his top 10 "mainstream" films of 2009, and it's easy to see why. Despite its unusual, some might say utilitarian conception, the movie has emerged as a highly distinctive character study which works both as a darkly humourous black comedy and as a breathlessly watchable thriller.

This is the movie that proves – if proof were needed – that Herzog's guerilla filmmaking instincts are not confined to working with tribes of natives in uncivilised regions of the earth. It is also an example of cinematic alchemy in its most remarkable form.