British nurse Pauline Cafferkey, who contracted Ebola in Sierra Leone, is no longer critically ill, the hospital treating her said.
The Scottish public health nurse remains in isolation at London's Royal Free Hospital where she is receiving specialist care.
She was diagnosed with Ebola after returning from Sierra Leone to Glasgow and was initially admitted to the city's Gartnavel Hospital on December 29, then transferred to London the following day.
Ms Cafferkey, from Cambuslang, South Lanarkshire, had volunteered with Save the Children at the Ebola Treatment Centre in Kerry Town, Sierra Leone.
She flew back to the UK via Casablanca in Morocco. Her temperature was tested seven times before she flew from Heathrow to Glasgow and she was cleared to travel.
She later became feverish and followed advice given to her at Heathrow to contact local services and was admitted to an isolation facility at the Brownlee unit in Gartnavel at 8am on December 29.
After a blood sample tested positive for Ebola, she was transferred in a military plane to the Royal Free.
The hospital said: "The Royal Free Hospital is pleased to announce that Pauline Cafferkey is showing signs of improvement and is no longer critically ill. She remains in isolation as she receives specialist care for the Ebola virus."
In a statement last week her relatives said: "We would like to thank all our friends, family and members of the public who have contacted us with support following Pauline's diagnosis with Ebola."
They thanked those working at the Royal Free, adding: "We want to thank all the staff caring for her for their kindness, support and compassion."
Ms Cafferkey's health deteriorated in the new year and on January 3 the hospital announced her condition was critical.
Officials from Public Health England and Health Protection Scotland are reviewing the UK's screening procedures for Ebola after it emerged she had been cleared to fly from London to Glasgow despite her temperature being checked seven times.
Her diagnosis has brought fresh scrutiny on the UK's preparedness for cases of Ebola, which can only be contracted by coming into contact with the bodily fluids of an infected person.
Previously, any possible Ebola carriers were advised to avoid crowded places and long journeys on public transport within the 21-day potential incubation period once they arrived back in the UK.