  Generally, stacking two quantum spin Hall insulators gives rise to a trivial
insulator. Here, based on first-principles electronic structure calculations,
we confirm that monolayer TaIrTe$_{4}$ is a quantum spin Hall insulator and
remarkably find that bilayer TaIrTe$_{4}$ is still a quantum spin Hall
insulator. Theoretical analysis indicates that the covalent-like interlayer
interaction in combination with the small bandgap at time-reversal invariant
$\Gamma$ point results in new band inversion in bilayer TaIrTe$_{4}$, namely,
the emergence of quantum spin Hall phase. Meanwhile, a topological phase
transition can be observed by increasing the interlayer distance in bilayer
TaIrTe$_{4}$. Considering that bulk TaIrTe$_{4}$ is a type-II Weyl semimetal,
layered TaIrTe$_{4}$ thus provides an ideal platform to realize different
topological phases at different dimensions.
