The genetic code has been analysed by a method similar to that used by Gregor Mendel. The current codon catalogue is shown to be symmetrically subdivisible into two discrete subcatalogues of eight quartets each by classifying the quartets as monocoding (for one amino acid only) vs heterocoding (for two amino acids or for amino acid plus nonsense). The internal symmetries of the two subcatalogues are identical, and are governed by two common parity rules. These rules, together with one governing the subdivision itself, can be explained by the hypothesis that two primaeval sets of polynucleotide-borne anticodons, corresponding closely but not exactly with the subcatalogues originated independently and separately (were not originally together within any replicating pre- or proto-biont). The discorrespondence between the primaeval sets and the subcatalogues is itself symmetrical, involving quartets sharing identical locations in the two subcatalogues. The primaeval sets correspond exactly with the subdivisions of the catalogue proposed by Skoog and co-workers on the basis of the presence vs the absence of cytokinins or “cytokininlike bases” adjacent to the anti-codons. A molecular model for the origin of the primaeval anticodon sets is described, and the relationship of the hypothesis with the origin of life, together with some possibilities for testing it, are discussed.