  Decoherence and non-Hermiticity are two different effects of the open quantum
systems. Both of them have triggered many interesting phenomena. In this paper,
we theoretically study an open two-level non-Hermitian system coupling to a
dissipative environment by solving the vectorized Lindblad equation. This
scheme provides us a powerful framework to address widespread open systems with
gain, loss and dissipation. Our results show that there exist a new class of
exceptional points (EPs) and steady states due to the interplay between
non-Hermiticity and decoherence. Furthermore, we also demonstrate new-type
topological properties of eigenstates with zero real-part of eigenvalues
($Re[\lambda]=0$) which are corresponding to Fermi arcs. It is revealed that
the phases of eigenstates located in Fermi arcs regime have a topological phase
$|\pi/2|$ which is totally unaffected by the dissipative environment. Our
results provide a promising approach for further uncovering and understanding
the intriguing properties of non-Hermitian open systems.
