'National Front?'

'Closely linked.' Halder smiled thinly. 'Fontaine's group targeted "social" opponents. Their identity photos covered the walls where he was shot. His blood was all over them. Greenwood had a nice sense of humour.'

'"Social" opponents.' I echoed Halder's ironic stress. 'Not rival candidates?'

'More the people who might vote for them. People with faces they didn't like.'

'Darker faces? Maghrebians?'

'Blacks, yellows, browns. Anything except pinko-grey. Faces like mine. People of the "other" side.'

'Who might canvass and vote for left-wing candidates. How did Fontaine and his people target them? I take it they used market-research firms?'

'Why bother? They saw them walking down the back streets in La Bocca and Mandelieu.'

'But they had their photos? It sounds very professional.'

'Mr Sinclair…' Halder surveyed me patiently. 'We're talking about coolie labour – factory hands, van drivers, building-site workers. The photos in Fontaine's office were taken after they were dead.'

'After…? How did they die?'

'All kinds of sudden ways. Traffic accidents, mostly. The back streets in La Bocca get very dark at night. It's easy for a truck to swerve. There's a squeal of tyres, and then the photoflash…'

'Halder – you've seen this?'

But Halder made no reply. He waved me away when I reached for the envelope of photographs. Since our arrival at the Bachelet house he had been trying to provoke me, but had succeeded only in provoking himself. He drummed at the gear lever, irritated that he had trapped himself within the loop of his own anger.

'Last one…' Halder turned off the avenue, so sharply that my head struck the window pillar. Without apology, he drove three hundred yards into the park, and stopped outside a dome-shaped building that housed the personnel department of Eden-Olympia. The ground-floor picture windows were filled with dioramas of lakeside apartments, and illuminated displays advertised vacancies for office juniors, cleaners and gardeners, the invisibles of Eden-Olympia, a population who left no shadows in the sun.

A party of hopefuls, mostly Spanish women in their best formal wear, dismounted from a bus, awed by the silent perfection of this lake and forest world. Halder watched them file into the building, shaking his head with the weary tolerance of a veteran eyeing a squad of callow recruits.

'Olga Carlotti…?' I took the photograph from Halder. 'She was director of personnel for the whole of Eden-Olympia. I assume Greenwood had no problems getting in to see her?'

'A doctor in a white coat isn't most people's idea of a serial killer. The security men saw him cross the lobby and said he looked normal. The place was filled with ushers, applicants coming out of interview booths, clerks checking social-security references. He showed his pass and went straight up to her.'

Death at Eden-Olympia seemed to come by flashlight, in the lens of a police photographer. Olga Carlotti lay across her desk, arms hanging loosely, ringed fingers almost touching the floor. She had been shot while inspecting a selection of passport-booth snaps. Blood from the bullet wound in the back of her head formed a mask of black lace across the features of a well-groomed Italian woman in her forties. A canted interior window looked down into the concourse below. The interview booths were empty, but a crowd of security guards, French police and office personnel stared up at the Carlotti office, watching the forensic team at work.

'I've seen enough.' Chilled by this last death, I handed the print back to Halder. 'Let's call it a day. Counting up all these murders is a nasty kind of arithmetic. Where were you at this time?'

'9.45? Driving with Captain Kellerman to the Siemens building. An armed man had tried to slip through the entrance on the garage roof. Someone parking a car said he saw a doctor with a rifle.'

' Greenwood? Did he enter the building?'

'Briefly. He reached the lobby but ran off when the security men challenged him. By now the general alert had gone out.'

Halder cruised along the central avenue, holding the Range Rover to the pace of a running man. For all his self-control, a fine sweat covered his amber skin, as if he were watching the murders inside his head and was even more disturbed by the replay.

He turned onto an access road that led to the multistorey garage behind the Siemens building. He raised the sun visor and pointed to the roof.

'There's a footbridge from the top deck to the senior executive offices. Security is light – it's a clever way to get in.'

'Who was the target?'

'No one knows – other companies share the building. Some president or CEO. We'll go up.'

'Halder, let's give it a rest. I know what a garage roof looks like.'

'This one is interesting…'

Ignoring me, Halder entered the garage and accelerated sharply. He swung the heavy vehicle past the parked cars, like a mountaineer making his final assault on the summit. Sweat drenched his uniform shirt as he pumped the brake pedal and forced the engine to labour in low gear. I sensed that he needed the Range Rover's howling supercharger to distract him from the private drama that had dogged him all afternoon.

We emerged onto the roof and swerved around an electrician's van that sat alone in the sun. Shielding my eyes, I thought of the white concrete searing Greenwood 's retinas as he stepped breathless from the staircase. Thirty feet away was the pedestrian bridge to the top three floors of the building.

Halder switched off the engine and lay back in his seat. I stepped out, and waited for him to join me, but he was staring at the parapet to our right. I walked around the car and leaned against his windowsill.

'So this is where it ended? Greenwood had killed seven people, and now he knew it was all over.' I pointed to the digital security panel beside the entrance. 'If the alert was on, his electronic passkey wouldn't have worked. How did he get into the lobby?'

'He called someone he knew – a woman in one of the offices. She came down and let him through.'

'Isn't that strange? There was a killer on the loose.'

'She didn't know it was Greenwood. His name had only gone out to the security teams. Some people say she tried to calm him down.'

'Brave woman. What was her name?'

'Madame Delmas. Very brave – and lucky. Greenwood had problems with his rifle.'

'He tried to shoot her?'

'That's what the security men said.' Halder noticed a face watching us from a window and lowered his visor. ' Greenwood was inside the lobby, trying to eject the empty magazine. When he put in a new clip the guards challenged him.'

A uniformed security man appeared at the glass doors, reluctant to test the heat of the open roof. He raised a hand in a deferential salute, as if Halder were a minor celebrity.

'You have an admirer,' I commented. 'In fact, you're quite a star.'

'I wouldn't say so. The guards here panicked a little.'

'But not you. So Greenwood backed away and disappeared into the garage, then somehow made his way to the villa?'

'That's it. End of story.'

'Almost.' I remembered the Riviera News transcript. 'He had less than five minutes to reach the villa and start killing the hostages. How did he manage it?'

Halder gestured evasively, trying to wipe the flood of sweat from his face and neck. 'Who knows? Maybe he stole a car – the garage is full of them. People forget their keys in the ignition.'

I waited for Halder to start the engine, but he seemed curiously reluctant to leave the roof. He stepped out and stared stonily at the glass curtain-walling, then walked towards the waist-high parapet.

His fists were clenched at his sides, his shoulders braced so tightly that the sweat-drenched fabric of his shirt seemed about to split.