Police are searching for a 34-year-old Brighton man called Carlo Dawes in connection with the murder of a man in Bevendean on Saturday morning.
A 37-year-old man was found by police collapsed inside a flat in Taunton Road Bevendean at about 5.20am after the police were called to the flat.
Paramedics were called to the scene but were unable to save his life and the victim was pronounced dead at the scene.
Police say they want to eliminate Carlo Nash from their enquiries. Mr Nash was known to the victim.
This is the second death in Brighton from a stabbing in a week. Last Sunday, Jeffrey Burrows was stabbed to death in his Norfolk Square flat. Joel Elliott, 22, of North Road, Brighton has now been charged with his murder and is in custody awaiting trial.
Detective Inspector Phil Mays, from the Surrey and Sussex Major Crime Team, said: "This is a tragic incident involving a small number of people who we believe were acquainted.
"We are keen to talk to Carlo Dawes in order to eliminate him from our inquiries.
"We are in the early stages of the investigation and are trying to establish the exact circumstances that led up to the victim receiving his fatal injuries.
"Although the suspect is outstanding we do not believe he is a threat to the wider public and we have committed a large number of resources in the hope of finding him soon.
"A police cordon and uniformed officers remain at the scene while forensic examinations of the flat and surrounding areas are carried out."
He urged anyone who knew Carlo Dawes's whereabouts to call Sussex Police on 101 or the independent charity Crimestoppers anonymously on 0800 111555.
Superintendent Steve Whitton, from the Brighton and Hove Command Team, said: "Our thoughts are with those who knew the deceased at this difficult time.
"This was an isolated incident but nonetheless we appreciate that people living in the Bevendean area will be concerned about the visible police presence.
"I would like to thank them for their patience and understanding and to further reassure them that our officers are doing all they can to find the person responsible for this crime."