  The non-Hermitian skin effect (NHSE) undermines the conventional
bulk-boundary correspondence (BBC) since it results in a distinct bulk spectrum
in open-boundary systems compared to the periodic counterpart. Using the
non-Hermitian (NH) Su-Schrieffer-Heeger (SSH) model as an example, we propose
an intuitive approach, termed ``doubling and swapping" method, to restore the
BBC. Explicitly, we construct a modified system by swapping the asymmetric
intracell hoppings in every second primitive unit cell, such that it has
double-sized unit cells compared to the NH SSH model and is free of NHSE.
Importantly, the modified system and the NH SSH chain exhibit identical spectra
under open boundary conditions (OBC). As a result, the modified system can
serve as the valid bulk for defining topological invariants that correctly
predicts edge states and topological phase transitions. The basic principle is
applicable to many other systems such as the non-Hermitian Creutz ladder model.
Furthermore, we extend the study to disordered systems in which the asymmetric
hoppings are randomly swapped. We show that two types of winding numbers can be
defined to account for the NHSE and topological edge states, respectively.
