The global Late Maastrichtian non-avian dinosaur apparent biodiversity is extensively surveyed for the first time. It amounts to 104 species (including unnamed forms) in 2010. The real biodiversity being obscured by taphonomical biases and the scarcity of the continental fossil record, a species-area relationship is used to estimate it. The results show that several hundreds (between 628 and 1078) non-avian dinosaur species were alive in the Late Maastrichtian, which is almost an order of magnitude above previous estimates. Because of the complex Late Cretaceous palaeobiogeography, discussions about dinosaur extinction should be based on this estimated real global biodiversity, not on the apparent biodiversity of a single area. Given the mean duration of dinosaur genera (7.7 Ma), the presence of so many dinosaur species in the Latest Cretaceous is consistent with the termination of most lineages at the Cretaceous-Tertiary boundary (the Late Maastrichtian sub-stage is 2.8 m.y. long). The Late Maastrichtian dinosaurian biodiversity is therefore consistent with the sudden extinction of the group following the Chicxulub impact.