  We theoretically study subgap states appearing at the interface between two
three-dimensional topological insulators which have different configurations in
the spin-orbit interactions from each other. The coupling of spin
$\boldsymbol{\sigma}$ with momenta $\boldsymbol{p}$ is configured by a material
dependent $3\times 3$ matrix $\boldsymbol{\Lambda}$ as ${\sigma}^\mu
{\Lambda}_\mu^\nu p_\nu$. We show that the spectra of the interface suggap
states depend strongly on the relative choices of $\boldsymbol{\Lambda}$ in the
two topological insulators. In particular, we focus on properties of gapless
states which appear when $\boldsymbol{\Lambda}$ in two topological insulators
are connected by the inversion in momentum space. We also discuss the
robustness of the gapless states under perturbations breaking the time-reversal
symmetry or the band-inversion symmetry by the numerical simulation.
