  We want to correct the misunderstandings on the tetrad (or veilbeins in
general) appeared in many text books or review articles. The tetrad should be
defined without any condition. $e_{\mu a}=\partial_\mu X_a$ with local Lorentz
coordinates $X_a$ ia wrong in many sences: it gives the condition $\partial_\mu
e_{\nu a}=\partial_\nu e_{\mu a}$, which leads us to the trivial result that
the cyclic coefficients vanish identically and to the null Riemannian tensor.
Also $e_{\mu a}e_\nu^a=g_{\mu\nu}$ is not scalar under the local Lorentz
transformation etc. We show how these deficits are remedied by the correct
definition, $e_{\mu a}=D_\mu Z_a$ with local (Anti) de Sitter coordinates
$Z_A$.
