A "probable" fifth Scottish case of swine flu is being tested as 19 further possible cases are under investigation.
The probable case is a woman in Fife who had recently returned from Las Vegas.
The majority of passengers who were on a flight to Glasgow with the fourth confirmed infected Scot have now been traced and are not showing symptoms.
But the Scottish Government said the overall situation could still move beyond containment to "mitigation".
A total of 27 cases have now been confirmed in the UK.
Health Secretary Nicola Sturgeon said the probable case was an individual who had travelled from Las Vegas to London and then on to Edinburgh on 30 April.
'Probable' fifth flu case in Fife
However, Ms Sturgeon stressed that she was not showing symptoms on either of those two flights.
Health officials have traced eight out of 10 "close contacts" who had been on the flight with the fourth confirmed Scottish case, as well as 40 of the other 47 passengers on the flight, all of whom were said to be not showing symptoms.
People who travelled with the man on Flybe flight BE7096 from Birmingham to Glasgow on Thursday were asked to contact the NHS.
Health Protection Scotland (HPS) said they may be at "low risk" of infection.
An HPS spokeswoman said: "We have done our own risk assessment and have been in touch with the vast majority of close contacts on the aircraft.
"We would ask that other passengers come forward and contact NHS 24 so they can be risk-assessed as a precaution."
She added that passengers currently in England or Wales should contact NHS Direct.
The fourth Scottish case of swine flu, officially known as the H1N1 virus, is unconnected to the three other cases, which were all linked.
Iain and Dawn Askham, from Polmont near Falkirk, became Britain's first confirmed cases on Monday 27 April after returning from their honeymoon in Mexico.
The third case, Graeme Pacitti from Falkirk, was confirmed four days later. He plays football with Mr Askham and they had been out drinking together.
The Scottish Government has meanwhile confirmed that Iain Askham attended a concert in Edinburgh days before he was treated for the virus.
He was among the crowd at the 1,500 capacity Picture House to see rock band Doves on Thursday 23 April, two days after he returned from his trip to Mexico and two days before he consulted a doctor about his flu symptoms.
The Scottish Government said this would not be classed as "close contact".
A spokesman said: "In line with Health Protection Scotland guidance, close contacts are followed up whenever any probable or confirmed cases are identified, to offer advice and where appropriate anti-virals.
"We are aware that Mr Askham did attend a concert on 23 April - before he was being treated - but this would not be classed as close contact.
"The risk of spread to others who were around him is low, and it is important to stress that the risk to public health in Scotland remains low."
Are you or is someone you know affected by the issues in this story? Send us your comments and experiences using the form below.
The BBC may edit your comments and not all emails will be published. Your comments may be published on any BBC media worldwide.
BBC NEWS CHANNEL
E-mail this to a friend
Printable version
BBC News
Bookmark with:
What are these?