The cumulative impact of enhancement technologies may alter the human species in the very long-term future. In this article, I will start showing how radical genetic enhancements may accelerate the conversion into a novel species. I will also clarify the concepts of ‘biological species’, ‘transhuman’ and ‘posthuman’. Then, I will summarize some ethical arguments for creating a transhuman or posthuman species with a substantially higher level of well-being than the human one. In particular, I will present what I shall call the Principle of the Best Interests of Posthumanity, which states that the enhancement of the human and transhuman species must be directed towards the creation of a posthuman existence that is substantially more valuable than its predecessors. I suggest that human extinction may be considered, within that principle, as one of the best interests of posthumanity. Finally, I will develop three objections that make that principle unattractive and that show that pursuing a full-blown programme of posthuman evolution is ethically flawed.