  We consider the role of non-triviality resulting from a non-Hermitian
Hamiltonian that conserves twofold PT-symmetry assembled by interconnections
between a PT-symmetric lattice and its time reversal partner. Twofold
PT-symmetry in the lattice produces additional surface exceptional points that
play the role of new critical points, along with the bulk exceptional point. We
show that there are two distinct regimes possessing symmetry-protected
localized states, of which localization lengths are robust against external
gain and loss. The states are demonstrated by numerical calculation of a
quasi-1D ladder lattice and a 2D bilayered square lattice.
