  We theoretically study emergent edge/corner localized states in monolayer
black phosphorene. Using the tight-binding model based on the density
functional theory, we find that the multi-orbital band structure due to the
non-planar puckered geometry plays an essential role in the formation of the
boundary localized modes. In particular, we demonstrate that edge states emerge
at a boundary along an arbitrary crystallographic direction, and it can be
understood from the fact that the Wannier orbitals associated with $3p_x$,
$3p_y$, $3p_z$ orbitals occupy all the bond centers of phosphorene. At a corner
where two edges intersect, we show that multiple corner-localized states appear
due to hybridization of higher-order topological corner state and the edge
states nearby. These characteristic properties of the edge and corner states
can be intuitively explained by a simple topologically-equivalent model where
all the bond angles are deformed to $90^{\circ}$.
