Despite the fact that DNA molecule is studied up and down, we know very little about the role of DNA triplets in coding amino acids and stop-codons. The paper aims to fill this gap through attracting spintronic ideas and carrying out QM/MM computations on a full-turn DNA fragment. The computations reveal two hidden symmetries: the spin splitting (the Rashba effect), confined within each triplet, and the quantum “phase” link between the triplet nature (in total, 64 triplets) and the corresponding amino acid and three stop-codons. The hidden symmetries become evident upon binding the magnesium cofactor to DNA triplets in 5’−3’ and 3’−5’ directions.