The Home Office said a group of girls aged between 15 and 17 who left a reception centre in France landed at Edinburgh airport on Saturday, without incident.
The children were brought to the UK by Home Office staff, with support from the local authority, under the Dubs amendment.
Several groups of unaccompanied refugee children have been transferred to England since October. An early group were taken to an immigration centre in Croydon where they were photographed and subjected to intense scrutiny by members of the rightwing media, who claimed some of them did not appear young enough.
Tory MP David Davies even called for dental checks to assess the refugees' ages.
Screens had to be erected in the London borough to protect later groups from paparazzi photographers and vitriolic headlines.
In contrast, the group of girls taken to Edinburgh are believed to have entered the UK without any trouble. The media was no notified until after they had arrived.
1,500 lone children were left unsupervised in Calais immediately after the camp they had been living in was demolished at the end of last month. The Home Office was accused of abandoning them, after they pulled out of the region and stopped processing the children's claims.
However the unaccompanied minors have now all been transported to reception centres in other parts of France and the Home Office has resumed assessments.
Home secretary Amber Rudd said priority is being given to Dubs amendment children who are under 12, who are likely to be granted refugee status in the UK, or who are at high risk of sexual exploitation.
The Home Secretary told Parliament that several hundred more children and young people will be brought to the UK.
The Home Office said those children who have come in under the criteria for the Dubs amendment, which requires the Government to give refuge to children stranded in Europe regardless of whether or not they have a family connection to the UK, will be placed, where possible, directly into the care of local authorities.
The Home Office will also continue to transfer eligible children with family links in the UK, under the Dublin Regulation.
A Home Office spokesman said: "We are continuing to work closely with the French Government and other partners to identify unaccompanied asylum seeking children who are eligible to come to Britain. As we have made clear, our focus is transferring these children as soon as possible and ensuring their safe arrival.
"After a brief pause during the clearance of the Calais camp, we can confirm the latest group of eligible unaccompanied minors has arrived in the UK.
"The Home Secretary informed Parliament last month that several hundred more children and young people will be brought to the UK in the coming weeks.
"So far more than 300 unaccompanied minors have been transferred to the UK."
The Home Office would not comment on how many children arrived at Edinburgh Airport.
It intends to confirm the total number of Dublin and Dubs transfers at the end of the process, when all of the transfers have taken place, Press Association reported.
Controversy has surrounded figures released in the past, with the charity Help Refugees claiming that Dublin agreement children — those with family in the UK — were counted under the new Dubs agreement — which is regarding children without a family connection to the UK — when they should not have been.
Scotland may be more welcoming to refugee children than England, where one in four local councils have said they will not take any unaccompanied minors because the government has not given them additional funding to cover the cost of their care.
Glasgow announced it would welcome 35 children from the Calais camp who have been identified as needing immediate help.
The local government in Edinburgh said it had costed how the capital could resettle 24 young people over a year. Under a formula proposed by the Home Office, Edinburgh would receive up to 56 unaccompanied refugee children.
Like in parts of England, there are issues with funding and the council would be expected to make up a large shortfall.
However, council leader Andrew Burns told the Edinburgh Evening News: “We will be taking our fair share of unaccompanied asylum-seeking children, absolutely definitely.”
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