Noting the scarcity of CpG dinucleotide in total genomic DNA derived from higher organisms and the scarcity of TpA dinucleotide in total genomic DNA derived from most life forms, we examined the distribution of these dinucleotides in sequences derived from functionally distinct types of human DNA, including mitochondrial DNA, intergenic DNA, intron DNA, and DNA destined to be represented in the cytoplasm as mRNA, tRNA, or rRNA. While CpG frequency has fallen to its lowest levels in DNA that is transcriptionally silent, TpA is most stringently excluded in DNA destined to be expressed as mRNA in the cytosol. This observation suggests that the selective pressures leading to the removal of CpG and TpA operate at different levels. With respect to TpA, dinucleotide scarcity may reflect a requirement for mRNA stability and may indicate the action of UpA-selective ribonucleases. We propose that, by reason of its instability, UpA must have been very rare in primordial RNA. Therefore, tRNA with the anticodon for this dinucleotide may have failed to evolve, making UpA the primordial doublet "stop" codon. The modern triplet code has faithfully conserved this arrangement in the two universal stop codons, UAA and UAG.