A murder inquiry is under way following the discovery of two bodies in a flat in north Belfast on Monday.
The victims were a 37-year-old woman, Frances Murray, and 47-year-old Joseph Dutton.
Their bodies were discovered at the property in Kinnaird Close at about 12:55 GMT, after a report was made by a member of the public.
A 35-year-old man arrested on Monday evening on suspicion of murder remains in police custody.
'Blood soaked clothes'
PSNI Det Ch Insp Peter Montgomery said police believed "some form of altercation took place within the flat where Frances and Joseph were found".
"I also want to locate a bag of blood soaked clothing that I believe was discarded in the local area," he said.
"The bag is described as being a white carrier type bag with orange lettering on it. If you see a bag matching this description please do not touch it and contact police immediately."
Det Ch Insp Montgomery appealed to anyone who was in the area at the time or who may have information about the incident to contact police.
He added the deaths were being treated as murder even though a post-mortem examination had yet to take place.
SDLP councillor Paul McCusker said it was "horrific news".
"There is a sense of shock across the community, a lot of anger, a lot of sadness," he said.
"Lots of children and lots of families live in this area. It is fairly settled."
Sinn Fein councillor JJ Magee said it was a "tragic scene".
"Absolutely shocked, the community is shocked by the news that has come from this very, very serious situation," he said.
Mr Magee said there would have been many children in the area around the time of the incident due to the Christmas holidays.