Steven Jackson and Michelle Higgins are alleged to have killed Kim Mackenzie at Jackson’s flat in Market Street, Montrose, Angus, some time between 26 October and 4 November.
They are said to have assaulted Miss Mackenzie by repeatedly striking her on the head with a hammer before striking her on the neck with a knife.
It is understood police are still searching for parts of Miss Mackenzie’s body, which it is understood was cut up and disposed of.
Jackson, 39, and Higgins, 28, of Lower Craigo Street, also from Montrose, appeared in private on petition at Forfar Sheriff Court yesterday.
They made no plea or declaration during brief, separate, hearings where they faced a single charge of murder.
Solicitors Nick Markowski, for Jackson, and Nick Wheelan, for Higgins, represented the pair.
Neither made any motion for bail.
Sheriff Donald Ferguson continued the cases against the pair for further examination and remanded both in custody.
They are expected to appear in court again next week.
No members of Miss Mackenzie’s family attended court for the calling of the case.
Parts of Miss Mackenzie’s body were found in a bin outside the property in Market Street last Thursday, sparking a major police investigation.
Jackson was detained immediately with Higgins being detained over the weekend.
It is understood she was located by police outwith Montrose on Saturday.
A major investigation was launched on Thursday, with Market Street and neighbouring John Street sealed off as forensic examiners in white suits carried out a detailed probe.
A recycling centre around one mile away on the town’s Bloomfield Road was also closed and sealed off by police as part of the investigation.
A Police Scotland spokeswoman said: “As part of the ongoing murder investigation in Montrose, police are able to confirm that human remains found during the evening of Wednesday, 4 November, 2015, have been identified as Kim MacKenzie, 37, from Montrose.
“The family of Kim MacKenzie have been updated with these latest developments and are being supported by family liaison officers.
“Officers have appealed to anyone who has any information to contact police.”