  Recently, based on the theory of teleparallel gravity, a simple and ghost
free parity violating gravity model was proposed in arXiv:2007.08038, where the
Weitzenb\"{o}ck connection was adopted for simplifying the calculations but
breaks the local Lorentz symmetry explicitly. In this paper, we restore the
local Lorentz symmetry of this model by giving up the Weitzenb\"{o}ck condition
or any other extra constraint on the connection. With full local Lorentz
covariance, this model is not a pure tetrad theory any more. We also apply the
new version of this model to the universe with general
Friedmann-Robertson-Walker background. This further generalizes the studies of
arXiv:2007.08038 where only the spatially flat background was considered.
Through the investigations of this paper, we confirm the results obtained in
arXiv:2007.08038 and in addition get some new results.
