The protein encoded by the vaccinia virusD4Rgene has base excision repair uracil–DNAN-glycosylase (vvUNG) activity and also acts as a processivity factor in the viral replication complex. The use of a protein unlike PolN/PCNA sliding clamps is a unique feature of orthopoxviral replication, providing an attractive target for drug design. However, the intrinsic processivity of vvUNG has never been estimated, leaving open the question whether it is sufficient to impart processivity to the viral polymerase. Here, we use the correlated cleavage assay to characterize the translocation of vvUNG along DNA between two uracil residues. The salt dependence of the correlated cleavage, together with the similar affinity of vvUNG for damaged and undamaged DNA, support the one-dimensional diffusion mechanism of lesion search. Unlike short gaps, covalent adducts partly block vvUNG translocation. Kinetic experiments show that once a lesion is found it is excised with a probability ~0.76. Varying the distance between two uracils, we use a random walk model to estimate the mean number of steps per association with DNA at ~4200, which is consistent with vvUNG playing a role as a processivity factor. Finally, we show that inhibitors carrying a tetrahydro-2,4,6-trioxopyrimidinylidene moiety can suppress the processivity of vvUNG.