We propose a non-Hermitian topological system protected by the generalized rotational symmetry which invokes rotation in space and Hermitian conjugation. The system, described by the tight-binding model with reciprocal imaginary next-nearest-neighbor hopping, is found to host two pairs of in-gap edge modes in the gapped topological phase, and is characterized by the non-Hermitian (NH) Chern number $C_{\mathrm{NH}}=2$. The quantization of the NH Chern number is shown to be protected by the generalized rotational symmetry ${\widehat{H}}^{+}\left(\mathrm{g}\vec{k}\right)={\widehat{U}}_g\widehat{H}\left(\vec{k}\right){\widehat{U}}_g^{+}$ of the system. Our finding paves the way towards non-Hermitian topological systems characterized by large values of topological invariants and hosting multiple in-gap edge states, which can be used for topologically resilient multiplexing.

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• Edge states
• Hall effect
• Topological insulators
• Topological materials
• Topological phases of matter