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We make a short comment on our new general relativity formulated on the Weitzenb\"ock space-time. The new general relativity considered here has one free parameter besides the Einstein constant. The total action is invariant under a class of local Lorentz transformations, besides being invariant under general coordinate and global Lorentz transformations. The consequences of this "restricted local Lorentz invariance" are studied.
Hayashi et al. (Tue,) studied this question.