A proof is given that the genes of the tRNA molecule of Nanoarchaeum equitans split into the 5' and 3' halves are an ancestral trait. First, the existence of a natural succession of evolutionary stages will be proven, formed in the order of the three gene structures of tRNAs known today: (i) the split genes of tRNAs, (ii) the genes of tRNAs with introns, and (iii) the genes of tRNAs continuously codifying for the tRNA molecule. This succession of evolutionary stages identifies the split genes of tRNAs as a pleisiomorphic character. The proof that this succession of evolutionary stages is, moreover, true is performed by proving that all the possible remaining five successions of evolutionary stages are false. Indeed, the succession of evolutionary stages considering split genes as a derived character turns out to be false in that the increase in complexity inherent to this succession cannot be justified by the split genes of tRNAs because these could not have conferred any selective advantage justifying this increase in complexity. Furthermore, genetic drift is unable to explain the evolution of split genes of tRNAs because of the enormous genetic effective size of the population observed in these organisms. The remaining four successions of evolutionary stages are also false because: (i) they are not natural successions of evolutionary stages, (ii) the absolute observed frequencies of these evolutionary stages are such as to exclude categorically that they might be natural successions of evolutionary stages, and also (iii) two of these are falsified by the fact that they do not place the evolutionary stage of genes of tRNAs with introns in a close evolutionary relationship with that of the split genes of tRNAs which can, instead, be proven to have a close evolutionary link. Therefore, there remains only the succession of evolutionary stages considering the split genes of tRNAs codifying for the 5' and 3' halves, as a pleisiomorphic character, as the only succession compatible with all the arguments presented in this article and as the one that actually operated during the evolution of the tRNA molecule. This proof has two very important implications. One regards how the tRNA molecule originated; considering how tRNA originated as the union of two hairpin-like structures, the split genes of tRNAs might be the transition stage through which the evolution of this molecule passed. The other regards when the genes of tRNAs originated, reaching the conclusion that the origin of these genes is polyphyletic, i.e. not monophyletic and hence contrary to the assumptions of the current paradigm.