A young woman goes to the police. She has a story to tell, but her story makes no sense. She has come to report that her boyfriend says he has killed a woman named Mary Trelease. But the person he says he has killed is indubitably alive. But the boyfriend insists he has killed her. Why would a man confess to a murder that never happened?

The Other Half Lives begins, then, with an impossible object, the psychological equivalent of the locked-room mystery, an apparently inexplicable event. What follows is in many ways a classic example of the crime thriller. Piece by suspenseful piece, more data about the hidden past are discovered, at first only making the case more baffling, but eventually untying the complex knot of secrets and deceptions until all is revealed. The significance of the title is only fully explained in the last sentence.

On the way to that satisfying (if not exactly happy) ending, you will enjoy most of the ingredients of the genre in its contemporary form. There is some snappy dialogue and a bit of gruesome violence. Wedded to the job, the assigned detective is juggling a personal life that is close to collapse. A disproportionate number of the characters are damaged by an experience of abuse, obsession or simple misery. It seems almost everyone is harbouring some secret shame or passion.

This is the fourth of Sophie Hannah's books to feature the odd couple of Charlotte Zailer and Simon Waterhouse. The story begins with their engagement party - not a success - but most of the time we watch them working together, though not exactly in harmony, as police colleagues.

The police force, as every crime-fiction reader knows, is a combination of back-stabbing sexist colleagues, bone-headed superiors and grinding paperwork. Our heroine, and hero, can only solve the crime by breaking the rules. Surely it's only a matter of time, we feel, before they are summoned by a superior officer and told, 'You're off the case.' All this is enjoyable, although Hannah's detectives are not so strongly drawn as to distract from the twists of the plot and the horribly creative mind of the killer.

The story takes us into the world of artists, gallery owners and the media. A painter has his first exhibition and his works are dispersed among buyers known to him only as names on a list. A journalist writes a feature on five up-and-coming artists whose lives become strangely intertwined. A failed comedian lands a job as a private investigator. A young man's flat is decorated with a collection of 16 empty picture frames. One painting may or may not be a disguised confession to murder.

You are going to need good powers of concentration to find your way through 500 pages or so of narrative in which a lot happens but most of which seems not to add up. However, when you reach the end you will see that Hannah does not cheat. Every strand of her complex story is unravelled. Unrelated and inexplicable events turn out to have been part of a credible sequence of cause and effect.

It is a remarkable piece of architecture and I don't know of another writer in the genre who constructs such baroque plots. The pleasure of suspense, of wanting to find out what happened, is the main reason why this kind of book is fun.

The question The Other Half Lives leaves us with is whether you can have too much of a good thing. Is it possible to have a surfeit of plot, like sitting down to a menu of unlimited oysters?