In this study, an improved method using scavenger-free plasmid DNA was established to accurately determine yields of DNA damage induced by direct and indirect actions of ionizing radiation. The scavenger-free plasmid DNA was obtained by dialysis over 5–7 days, and the DNA solvent was replaced with phosphate buffer to completely remove impurities, which could be scavengers of radicals produced as a result of water radiolysis. DNA samples of films and dilute aqueous solutions were used to separately evaluate contributions of the direct and indirect actions of X rays (150–160 kVp). The irradiated DNA was analyzed by agarose gel electrophoresis to quantify strand-break yields. The yields of single-strand breaks (SSBs), n(SSB), were determined to be (6.5 ± 2.0) × 10^–10 and (3.1 ± 0.9) × 10^–7 SSBs/Gy/Da for the film and solution samples, respectively, showing a significant contribution of hydroxyl radicals (^•OH) compared with direct energy depositions from ionizing radiation to DNA. As observed in SSBs, the yields of double-strand breaks (DSBs), n(DSB), were (5.6 ± 1.1) × 10^–11 and (1.3 ± 0.2) × 10^–8 DSBs/Gy/Da for the film and solution samples, respectively. The yield ratio of DSBs to SSBs, that is, n(DSB)/n(SSB), was 0.091 ± 0.026 for the film samples, while it was much lower for the solution samples (0.045 ± 0.010), indicating that direct actions result in more localized strand breaks relative to indirect actions. Base excision repair enzymes, namely, endonuclease III (Nth) and formamidopyrimidine-DNA glycosylase (Fpg), were utilized after irradiations to convert base lesions and apurinic/apyrimidinic (AP) sites into strand breaks. The amounts of Nth and Fpg for the conversion were optimized to a few units per µg of DNA, although the optimal concentrations can differ among conditions.