From NYTimes:
An improvement in the dating of fossils suggests that the Neanderthals, a heavily muscled, thick-boned human species adapted to living in ice age Europe, perished almost immediately on contact with the modern humans who started to enter Europe from the Near East about 44,000 years ago. Until now bones from several Neanderthal sites have been dated to as young as 29,000 years ago, suggesting there was extensive overlap between the two human species. This raised the question of whether there had been interbreeding between humans and Neanderthals, an issue that is still not resolved.
But researchers report that tests using an improved method of radiocarbon dating, based on a new way to exclude contaminants, show that most, and maybe all, Neanderthal bones in Europe are or will be found to be at least 39,000 years old....