Although it has previously been shown that Neanderthals contributed DNA to modern humans(1,2), not much is known about the genetic diversity of Neanderthals or the relationship between late Neanderthal populations at the time at which their last interactions with early modern humans occurred and before they eventually disappeared. Our ability to retrieve DNA from a larger number of Neanderthal individuals has been limited by poor preservation of endogenous DNA(3) and contamination of Neanderthal skeletal remains by large amounts of microbial and present-day human DNA(3-5). Here we use hypochlorite treatment(6) of as little as 9 mg of bone or tooth powder to generate between 1- and 2.7-fold genomic coverage of five Neanderthals who lived around 39,000 to 47,000 years ago (that is, late Neanderthals), thereby doubling the number of Neanderthals for which genome sequences are available. Genetic similarity among late Neanderthals is well predicted by their geographical location, and comparison to the genome of an older Neanderthal from the Caucasus(2,7) indicates that a population turnover is likely to have occurred, either in the Caucasus or throughout Europe, towards the end of Neanderthal history. We find that the bulk of Neanderthal gene flow into early modern humans originated from one or more source populations that diverged from the Neanderthals that were studied here at least 70,000 years ago, but after they split from a previously sequenced Neanderthal from Siberia(2) around 150,000 years ago. Although four of the Neanderthals studied here post-date the putative arrival of early modern humans into Europe, we do not detect any recent gene flow from early modern humans in their ancestry.