In the present study, we consider the formation of a single strand break (SSB) in DNA via an alternative mechanism involving O-P bond splitting that was observed as a minor route to DNA damage induced by low-energy electrons (LEEs) or gamma radiation. We postulate and characterize, at the B3LYP/6-31+-1-G** level, a path that starts with LEE attachment to the nucleotide of thymine resulting in a stable valence radical anion localized on pyrimidine. In the next step, a proton is attached to the CS position of thymine, producing a neutral monohydroradical of this nucleotide. This event triggers the subsequent intramolecular transfer of a sugar hydrogen atom from C3' or CS' to the C6 site of thymine. In the final elemental reaction, O-P bond dissociation takes place, which yields the phosphoryl radical and a cyclic ketone or aldehyde. Identification of the latter species as well as 5,6-dihydropyrimidines in DNA solutions irradiated with ionizing radiation could provide experimental confirmation of the suggested mechanism.