  We propose an anti-parity-time (anti-PT ) symmetric non-Hermitian
Su-Schrieffer-Heeger (SSH) model, where the large non-Hermiticity
constructively creates nontrivial topology and greatly expands the topological
phase. In the anti-PT -symmetric SSH model, the gain and loss are alternatively
arranged in pairs under the inversion symmetry. The appearance of degenerate
point at the center of the Brillouin zone determines the topological phase
transition, while the exceptional points unaffect the band topology. The large
non-Hermiticity leads to unbalanced wavefunction distribution in the broken
anti-PT -symmetric phase and induces the nontrivial topology. Our findings can
be verified through introducing dissipations in every another two sites of the
standard SSH model even in its trivial phase, where the nontrivial topology is
solely induced by the dissipations.
