Nanotubes of hexagonal boron nitride (h-BN) have been synthesized by are discharge between ZrB2 electrodes in a nitrogen atmosphere. A new morphology of BN nanotubes at their tips, exhibiting a "triangular flag" like shape, was observed by transmission electron microscopy. This morphology suggests the presence of energetically unfavorable odd-membered rings (e.g., pentagons and heptagons) in addition to favorable even-membered rings (e.g., squares).