  Topology plays an important role in non-hermitian systems. How to
characterize a non-hermitian topological system under open-boundary
conditions(OBCs) is a challenging problem. A one-dimensional(1D) topological
invariant defined on a generalized Brillion zone(GBZ) was recently found to
successfully describe the topological property of the two-band
Su-Schrieffer-Heeger model. But for a 1D multi-band chiral symmetric system
under OBCs, it is still controversial how to define the topological invariant.
We show in this letter by exact proof and detailed demonstration that to
acquire the topological invariant for multi-band non-hermitian models with
chiral symmetry, the GBZ as the integral domain should be replaced by a more
generalized closed loop. Our work thus establishes the non-Bloch bulk-boundary
correspondence for 1D multi-band chiral symmetric non-hermitian systems.

Strongly Correlated Electrons;Mesoscale and Nanoscale Physics;Materials Science;Other Condensed Matter;Quantum Physics