  The skin effect and topological edge states in non-Hermitian system have been
well-studied, and the second-order skin effect and corner modes have also been
proposed in non-Hermitian system recently. In this paper, we construct the
nested tight-binding formalism to research the second-order corner modes
analytically, which is a direct description of the generic non-Hermitian
tight-binding model without other assumptions. Within this formalism, we obtain
the exact solutions of second-order topological zero-energy corner modes for
the non-Hermitian four-band model. We validate the nested tight-binding
formalism in the hybrid skin-topological corner modes for the four-band model
and a non-Hermitian two-dimensional (2D) extrinsic model. In addition, we
exactly illustrate the corner modes induced by second-order skin effect for a
simplest 2D non-Hermitian model by the nested tight-binding formalism.
