We analyse 6,810 tRNAs, calculating the free energy of the corresponding double hairpin and 'cigar' secondary structures, for which we find a high thermodynamic and statistical significance. We also analyse these tRNAs for similarity and complementarity of their 5' and 3' halves or segments of them in intra-and inter-molecular comparisons. We find very clear signs that the two halves of tRNAs had an evident evolutionary relationship, although it is not totally clear whether this was a relationship of homology or complementarity between the 5' and 3' halves of tRNAs, even if there is strong evidence in favour of the homology hypothesis. Overall, these data favour models for the origin of the tRNA molecule postulating that a duplication event involving a hairpin structure as a precursor was involved in the origin of this molecule. Moreover, we interpret these results and favour the hypothesis that sees the assembly of two hairpin structures sharing a homology relationship as the intermediate evolutionary stage preceding the appearance of the cloverleaf structure of tRNA.