A Thai woman who recently died of bird flu probably caught the disease from her daughter, the government has said.
Millions of birds have been culled to try to stem the spread of the virus
If true, she would be the first person in the latest outbreak to get bird flu from another human rather than birds.
A case of human-to-human infection would renew fears that bird flu may one day combine with human flu to create a more deadly version of the disease.
But officials said this was likely to be an isolated case, and the WHO said it posed no "significant" public risk.
Klaus Stohr, head of the WHO's global influenza programme, said the latest case was possibly another example of a "non-sustained, inefficient, dead-end-street,
But he said the WHO was still concerned in case the case was the beginning of a more widespread transmission.
Pranee Thongchan, 26, died of the H5N1 bird flu virus on 20 September, shortly after her daughter is believed to have died of the same illness, Thailand's Ministry of Public Health said.
H5N1 BIRD FLU VIRUS
Principally an avian disease, first seen in humans in Hong Kong, 1997
Almost all human cases thought to be contracted from birds
Isolated cases of human-to-human transmission in Hong Kong and Vietnam, but none confirmed
The daughter, Sakuntala, was cremated before tests were conducted, so it will never be known for certain that she had the virus.
A statement from the Public Health Ministry said Pranee Thongchan: "either contracted the virus from the environment in the village where the chickens died, or from the sick daughter who she was taking care of very closely at the hospital for a long period of time".
Pranee's sister, Pranom - who also looked after Sakuntala in hospital - was confirmed as suffering from bird flu on Monday, and is now recovering in hospital.
The ministry statement stressed that the family's case was an isolated one.
"This probable human-to-human
transmission of avian influenza was related to a single index case and was limited within a family," it said.
To reassure those who fear a human-to-human link could lead to a new virulent strain of the virus, the statement added: "There is no evidence to suggest that the virus has
mutated or re-assorted."
This is not the first suspected case of human-to-human transmission of bird flu.
In previous epidemics - such as that in Hong Kong in 1997 and an outbreak in several parts of Asia last year - officials were unable to rule out the possibility that a very small number of victims had contracted the disease from other humans.
'Crisis of global importance'
At least nine other people have died from bird flu in Thailand so far this year - and a further 19 in Vietnam - but all are thought to have contracted the disease from poultry.
Tens of millions of chickens and other poultry have already been killed by the disease, or culled in an attempt to stop the disease spreading.
Two UN agencies warned on Monday that bird flu was set to remain a serious threat to animal and human life worldwide for some time to come.
Bird flu was a "crisis of global importance", the UN Food and Agriculture Organization (FAO) and the World Organization for Animal Health (OIE) said in a joint statement.
They stressed that the virus continued to circulate in East Asia and urged governments to take more action.
While stressing that culling was the best way to tackle the problem, they added that
vaccination against bird flu could be used as a complementary measure.
The BBC's science correspondent, Richard Black, says the warning by the UN-affiliated bodies is unusually stark.