  We investigate the "pole-skipping" phenomenon in holographic chaos. According
to the pole-skipping, the energy-density Green's function is not unique at a
special point in complex momentum plane. This arises because the bulk field
equation has two regular near-horizon solutions at the special point. We study
the regularity of two solutions more carefully using curvature invariants. In
the upper-half $\omega$-plane, one solution, which is normally interpreted as
the outgoing mode, is in general singular at the future horizon and produces a
curvature singularity. However, at the special point, both solutions are indeed
regular. Moreover, the incoming mode cannot be uniquely defined at the special
point due to these solutions.
