A specialist team found progress had been made at Edinburgh's Bupa-run Pentland Hill nursing home but called for standards to be raised more quickly.
Police have submitted a report to the procurator fiscal following a separate investigation into four deaths at the home.
The Care Inspectorate issued an improvement notice last year after inspectors raised serious concerns in an unannounced visit to the premises, which remains closed to new admissions.
The home was warned it faced closure unless standards were raised.
Inspectors who visited on December 20 found the home had made improvements to bedding, nutrition and the way medicines were administered and recorded. The garden had been made safe and complaints were being handled properly, they said.
Dr Robert Peat, director of inspection, said: "We have seen evidence of changes in how Pentland Hill is run, including a new manager, which is welcome.
"Overall, the home has made some progress but we need to see greater and faster improvements so the changes are sustained and consistent. Every person is entitled to high-quality, safe care that is compassionate."
The home has until the end of this week to make further improvements.
A spokeswoman for Pentland Hill Care Home said: "We're pleased that the Care Inspectorate's inspection, which was carried out in December, found that there were improvements within the home. These have also been recognised by our residents and their families.
"We continue to work hard to ensure all improvements are sustained and that we're delivering a consistently high standard of care to our residents."