The compound UPtGe is the only $5f$ system known to possess an incommensurate helical structure. The nature of this unique magnetic structure is studied within density-functional theory, and we show that the formation of a helical arrangement results from the coexistence of accidentally small in-plane magnetic anisotropy and frustrated exchange interactions. The system is not, however, a pure exchange helix since the Dzyaloshinski-Morija interaction plays an important role and the magnetic structure possesses features inherent only for relativistic helices.