  The restoration of spin connection clarifies the long known local Lorentz
invariance problem in telelparallel gravities. It is considered now that any
tetrad together with the associated spin connection can be equally utilized.
Among the tetrads there is a particular one, namely proper tetrad, in which all
the spurious inertial effects are removed and the spin connection vanishes. A
specific tetrad was proposed in the literature for spherically symmetric cases,
which has been used in regularizing the action, as well as in searching
solutions in various scenarios. We show in this paper that the this tetrad is
not the unique choice for the proper tetrad. We construct a new tetrad that can
be considered as the proper one, and it will lead to different behaviors of the
field equation and results in different solutions. With this proper tetrad, it
is possible to find solutions to teleparallel gravities in the strong field
regime, which may have physical applications. In the flat spacetime limit, the
new tetrad coincides with the aforementioned one.
