  An unpaired gapless Dirac electron emergent at the surface of a strong
topological insulator (STI) is protected by the bulk-surface correspondence and
believed to be immune to backward scattering. It is less obvious, however, and
yet to be verified explicitly whether such a gapless Dirac state is smoothly
extended over the entire surface when the surface is composed of more than a
single facet with different orientations in contact with one another at sharp
corner edges (typically forming a steplike structure). In the realistic
situation that we consider, the anisotropy of the sample leads to different
group velocities in each of such facets. Here, we propose that much insight on
this issue can be obtained by studying the electronic states on a hyperbolic
surface of an STI. By explicitly constructing the surface effective
Hamiltonian, we demonstrate that no backward scattering takes place at a
concave $90^\circ$ step edge. A strong renormalization of the velocity in the
close vicinity of the step edge is also suggested.
