Euphorbia rimireptans, here described as a new species, is known only from the northern part of the Skeleton Coast (part of the Namib Desert) in the Kaokoveld Centre of Endemism, northweste Namibia. These perennial shrublets grow on rocky outcrops of latite under harsh desert conditions. Diagnostic characters for E. rimireptans include the procumbent, sometimes pendant habit, the soft, rubber-like terete or slightly tapering branches that are curved or ± straight, frequently orientated in the same direction from the base, and the glabrous or sparsely hairy capsule, which releases verrucose ovoid seeds. A comparison of some of the more prominent morphological features to differentiate between E. rimireptans and its possible nearest relative, E. giessii, is provided. Keywords: endemism, flora, Kaokoveld Centre of Endemism, latite, Namib Desert, taxonomy.