Seven people from the same family in northern Sumatra, Indonesia, died from the disease earlier this month.
WHO spokesman Peter Cordingley said there was no sign of diseased poultry in the immediate area.
Investigators are looking into the possibility that the virus spread from human to human, Mr Cordingley said.
But he emphasised that there was no indication the virus had mutated.
Experts are worried that if it does mutate, the H5N1 strain could become more easily transmitted between humans, leading to a worldwide pandemic of the killer disease.
The H5N1 virus has already killed more than 120 people worldwide since 2003. It has also devastated poultry stocks.
The majority of deaths have occurred in Asia, but cases in people and birds have also been recorded in Europe and Africa.
Almost all human infections so far are thought to have been caused by direct contact with sick poultry.
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News Health Avian flu Bird flu H5N1 Pandemic Influenza Spanish Flu WHO Flu Indonesia
