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Canterbury District Health Board medical officer of health Dr Cheryl Brunton said these are 12 residents and eight staff.
All of the rest home's 64 residents are being treated as close contacts and will be tested if they display symptoms of Covid-19.
On Tuesday, 12 residents and four staff at the rest home had either tested positive for the virus or been identified as probable cases.
Said Dr Brunton: "Of the 44 residents and staff remaining at Rosewood rest home, there have been no confirmed/probable cases of Covd-19."
She said the rest home's other 20 residents have been relocated to Burwood Hospital "because it is an appropriate space for them to self-isolate together as a ‘bubble’, not because they require hospital-level care."
Dr Brunton did not say how many Rosewood residents have recovered from the virus but said: "Details of COVID-19 hospitalisations and cases that have recovered across New Zealand can be found on the Ministry of Health’s website."
Meanwhile, there have been no new cases of Covid-19 at a Christchurch rest home where two residents tested positive.
The two residents with the virus who live at George Manning Lifecare & Village in Spreydon are said to be recovering well and are expected to be out of isolation as early as next week.
The remainder of the rest home's about 80 residents have been in isolation since an 87-year-old woman was discovered as the first case, shortly followed by another woman. They should also be out of isolation next week.
Said Norah Barlow, chief executive of Heritage Lifecare, which owns and operates the rest home: "There are no new cases, there are no more positive tests and the people are absolutely doing exceptionally well.
"The residents [with Covid-19] have been doing very well and we're planning on them coming out of isolation early next week as well."
The total number of Covid-19 cases in the Canterbury District Health Board area has grown by five in the last 24 hours, with the region's total now standing at 119.
During Thursday's update, Director General of Health Ashley Bloomfield revealed there were 29 new confirmed and probable cases of Covid-19 in New Zealand over the past 24 hours.
The CDHB area continues to have the fifth-highest number of cases behind the Southern, Waitemata, Waikato and Auckland DHBs.
The combined total of confirmed and probable cases in New Zealand is 1239.