A novel tubular form of graphitic boron nitride (BN) displaying a hollow conical-helix was discovered. It was generated via wrapping a single beltlike filament according to the geometry of an Archimedes spiral. Cone apex angles of helical-conical nanotubes (HCNTs) were found to exhibit specific values, each of which refers to a certain coincidence site lattice. A unique structural property of HCNTs was observed, displaying the transformation of apex angles during the annealing process. The observed apex angles were reduced with decreasing annealing temperature, which is in accordance with an estimated HCNT strain energy decrease for a given tubular radius. It is suggested that the curvature and apex angle of a HCNT are determined by a sole dynamic element, that is, enthalpy (DeltaH), whereas the HCNT disclination configuration changes through helical sliding of the filament.