  Exceptional point (EP) associated with eigenstates coalescence in
non-Hermitian systems has many exotic features. The EPs are generally sensitive
to system parameters, here we report symmetry protected isolated EPs in the
Brillouin zone (BZ) of a two-dimensional non-Hermitian bilayer square lattice;
protected by symmetry, the isolated EPs only move, merge, and split in the BZ.
The average values of Pauli matrices under the eigenstate of system Bloch
Hamiltonian define a real planar vector field, the topological defects of which
are isolated EPs associated with vortices. The winding number characterizes the
vortices and reveals the topological properties of the non- Hermitian system.
Different topological phases correspond to different EP configurations, which
are unchanged unless topological phase transition occurs accompanying with the
EPs merging or splitting.
