Police believe the killer responsible for the New Year's Day murder in Phillip was known to his victim and stole his mobile phone, using it to make calls after the attack.
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Investigations into the killing of Miodrag Gajic, 71, are continuing, with police saying they are making ''positive progress'' on the case.
Mr Gajic was found dead with ''significant'' head injuries in his Mansfield Place unit just before 2pm on New Year's Day.
Friends had come to see him earlier in the day and became concerned when they couldn't raise him.
Neighbours, who described Mr Gajic as a ''good bloke'', reported hearing a terrible scream as his body was discovered. Police believe Mr Gajic was killed between 10.40am and 11.30am, meaning he lay dead for hours before being found.
The victim is thought to have known the attacker on some level. Police also suspect that the killer took Mr Gajic's mobile phone, and used it after the death.
Neighbours said Mr Gajic was known to have regularly dealt cannabis.
The investigation into his death is now in its fourth week.
Police have identified a suspect in the killing, and he is no longer at liberty because of separate offences.
Last week, police searched scrubland in Red Hill near Hindmarsh Drive for almost an entire day, looking for items linked to the murder.
Police said they found a number of items that would be subjected to forensic testing. Also last week, investigators went public with a call for two women, whom they believed to be key witnesses, to come forward.
The women possibly saw Mr Gajic's killer entering or leaving the small apartment complex.
It is not known whether police believe a weapon was used in the killing, and the exact nature of Mr Gajic's injuries is not clear.
Mr Gajic's death came less than a week after the discovery of the body of Nicholas Sofer-Schreiber in his Lyneham unit.
Mr Sofer-Schreiber was stabbed to death in his home, just opposite the Lyneham shops, some time before December 28.
Friends found the punk fan's body when they went to his home after he had not been seen since Boxing Day.
Police, aided by Mr Sofer-Schreiber's friend and former housemate, last week called for the public to come forward with additional information.
Anyone with information on the killings should contact Crime Stoppers on 1800 333 000 or through the website.
