Many tRNA molecules that recognize the purine-ending codons but not the pyrimidine-ending codons have a modified uridine at the wobble position, in which a methylene carbon is attached directly to position 5 of the uracil ring. Although several models have been proposed concerning the mechanism by which the 5-substituents regulate codon-reading properties of the tRNAs, none could explain recent results of the experiments utilizing well-characterized modification-deficient strains of Escherichia coli. Here, we first summarize previous studies on the codon-reading properties of tRNA molecules with a U derivative at the wobble position. Then, we propose a hypothetical mechanism of the reading of the G-ending codons by such tRNA molecules that could explain the experimental results. The hypothesis supposes unconventional base pairs between a protonated form of the modified uridines and the G at the third position of the codon stabilized by two direct hydrogen bonds between the bases. The hypothesis also addresses differences between the prokaryotic and eukaryotic decoding systems.