  A second-order topological insulator on a two-dimensional square lattice
hosts zero-dimensional states inside a band gap. They are localized near
$90^{\circ}$ and $270^{\circ}$ corners constituting an edge of the system. When
the edge is in a staircase form consisting of these two corners, two families
of edge states (i.e., one-dimensional states localized near the edge) appear as
a result of the hybridization of zero-dimensional states. We identify symmetry
that makes them gapless. We also show that a pair of nontrivial winding numbers
associated with this symmetry guarantee a gapless spectrum of edge states,
indicating that bulk--boundary correspondence holds in this topological
insulator with a staircase edge.
