Abstract. In the work it is shown that 20 protein amino acids ("the canonical amino acids" within the genetic code) appear to be a whole and very symmetrical system, in many ways, all based on strict chemical distinctions from the aspect of their similarity, complexity, stereochemical and diversity types. By this, all distinctions are accompanied by specific arithmetical and algebraic regularities, including the existence of amino acid ordinal numbers from 1 to 20. The classification of amino acids into two decades (1-10 and 11-20) appears to be in a strict correspondence with the atom number balances. From the presented "ideal" and "intelligent" structures and arrangements follow the conclusions that the genetic code was complete even in prebiotic conditions (as a set of 20 canonical amino acids and the set of 2+2 pyrimidine / purine canonical bases, respectively); and the notion "evolution" of the genetic code can only mean the degree of freedom of standard genetic code, i.e. the possible exceptions and deviations from the standard genetic code. [This is the second version with minimal interventions in the text. In addition, one passage was added in front of the second star, with quoting of T. Jukes. Added is Remark 4 and a more adequate shading in the From a chemical point of view the first step of classification of protein amino acids (AAs), "the canonical amino acids" within genetic code, must be the classification into aliphatic and aromatic AAs, where on a hierarchical scale of changes by similarity and complexity, aliphatic AAs must precede the aromatic. For the same reason of the chemical hierarchy, within the class of aliphatic AAs at the beginning must be the hydrocarbon AAs (possesing in the side chain carbon and hydrogen, or hydrogen only, in the case of glycine), and at the end two sulfur AAs, quite different from preceded non-sulphuric AAs. This means that two sulfur AAs [as last in class of aliphatic AAs] must be found in a direct contact to the aromatic ones.In further course of sequencing of AAs, in terms of changes by similarity, from the aspect of the AAs singlets and/or doublets, i.e. pairs, it should be considered appropriate distinctions in three areas: in the hydrocarbon, aromatic, and that between them. In the set of aromatic AAs, Phe came first, as the simplest, followed by Tyr, and Trp, all three with possession of a benzene ring. At the very end ultimately must be His, the only one who does not possess the aromatic benzene ring. In the set of hydrocarbon AAs, at the very beginning must be Gly as the simplest one. Follows Ala as the first possible case of hydrocarbon series with an open carbon chain. Then come Val and Pro, both with three carbon atoms in the side chain, rather than Leu and Ile with four carbon atoms. By this, Val with half-cyclic chain precedes Pro with cyclic one; also Ile precedes Leu, as more similar with Pro. [The details of the relationship between Val and Pro, see in: Rakočević & Jokić, 1996; on the relationship between Pro and Ile, in: Rakočević 1998, Survey 4,...