The first Neanderthal complete genome published in 2014 is that of a woman living on Mount Altai. From a single sequenced diploid individual, it is possible to infer the demography of the species to which it belongs. Thus, in the original publication of this genome, they propose a demographic scenario suggesting that this woman would be one of the last representatives of Neanderthals. Strange. Moreover, the proposed demography ignores a possible structuring of the Neanderthals. However, Jean-Pierre never ceased to insist that Neanderthal lived in tribes of about twenty individuals. By re-analyzing the data of this first Altai genome, we have been able to show that the proposed demography could actually be the only fact of a spatial structuring. Thus, the pattern observed is entirely compatible with a totally stable demography of weakly connected tribes, without any variation in the total number of individuals. This study illustrates the absolute necessity of incorporating archaeological knowledge to carry out a relevant genetic study.