Coastguards found a blue plastic barrel near the murder victim
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Police are trying to identify a man found on rocks with his hands and feet tied and a plastic bag over his head.
It was one of three bodies found on Friday at Beachy Head near Eastbourne, but the deaths are not being linked.
A post mortem examination has shown the man died from multiple stab wounds.
Detective Chief Inspector Tony O'Donnell, of Sussex Police's major crime branch, said they believed the man had died on either Wednesday or Thursday.
The body may have been thrown over the cliff in a barrel found nearby, he said.
Mr O'Donnell described the man as being black, aged around 30, 5 ft 8 in tall, with a full Afro hairstyle and full black beard.
He was of slim, athletic build and wore a black Performance Wear coat, black Groove Armada zip-up top and blue jeans.
Sussex Police have set up Operation Dundee to investigate the murder and have appealed for help to identify the victim.
"We are sure that the murder happened away from the scene," said Mr O'Donnell.
"It could have happened anywhere before his body was dumped over Beachy Head.
Identity plea
"I would ask anyone with a partner, family member or friend who has not been seen for the past few days to contact our incident room."
He added: "We need to identify him as soon as possible."
Forensic tests are being carried out on the 220-litre, blue plastic barrel found near the body.
Officers are also trying to trace the man using fingerprints, DNA and missing person records, as well as information from other police forces.
A body was first seen on rocks at the foot of the 600-feet-high cliffs by the crew of a Sussex Police helicopter just before 1500 GMT on Friday.
Routine patrol
When they flew past the cliffs again on routine patrol, the pilot saw the other corpses.
On Saturday cliff rescue specialists were lowered to the remains, which were all found within 50 feet (15 metres) of each other.
A police spokesman said on Sunday the identities of the other two bodies had not yet been established.
But he said their deaths were not regarded as suspicious and they were not believed to be linked.
Officers believe the bodies entered the water
at different times because all three displayed varying levels of decomposition.
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We are sure that the murder happened away from the scene
