The patient from Lanarkshire is undergoing a procedure where blood is circulated outside the patient`s body and oxygen added artificially.
The same treatment - called extra corporeal membrane oxygenation (ECMO) - was giving to pregnant mother Sharon Pentleton in July after she suffered an extreme reaction to the H1N1 virus.
Ms Pentleton, who made a full recovery, was taken to Sweden because no beds were available at the UK specialist unit in Leicester.
The Scottish Government revealed the latest development as part of a weekly update which showed about 1,000 Scots are now catching the virus each day.
Health officials said about 7,034 people caught H1N1 in the past week, up from about 6,180 the previous week.
The rate of GP consultations for flu-like illnesses was 62.1 per 100,000 people, an increase from last week`s figure of 53.3.
As of Wednesday, 165 people with swine flu had been hospitalised since the start of the outbreak.
Health Secretary Nicola Sturgeon said: “The potential threat from H1N1 remains serious, even if it continues to be a relatively mild virus.
“Vaccination is the best defence we have against the H1N1 virus and Scotland is preparing very well for the vaccination programme.”
Health Protection Scotland revealed it wants to blood test children to track the spread of swine flu and discover if people are building up immunity.
School children were picked because they have proved most susceptible to the H1N1 infection.
Only one or two secondary schools would need to take part in the tests, which would be voluntary.
A Government spokesman said: “With a new virus like H1N1, it`s incredibly important for public health that we learn as much about how it behaves as possible.
“This study is designed to give public health doctors an insight into how to manage outbreaks in schools and other communities.
“It makes sense to carry out surveillance where possible and where parents and children are happy to give consent.”
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