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Modified gravity which was constructed by torsion scalar $T$, namely $f(T)$doesn't respect Lorentz symmetry. As an attempt to make a new torsion basedmodified gravity with Lorentz invarianve, recently $f(T,\mathcal{B})$introduced where $B=2\nabla_{\mu}T^{\mu}$ \citep{Bahamonde:2015zma}. We wouldargue, even when all is constructed and done in a self-consistent form, if youhandle them properly,we observe that there is no Lorentz invariant teleparallelequivalent of $f(R)$ gravity. All we found is that the $f(R)$ gravity in which$R$ must be computed in Weitzenb\"{o}ck spacetime, using Weitzenb\"{o}ck'sconnection, nor Levi-Civita connections is the only possible Lorentz invarianttype of modified gravity. Consequently, $f(T)$ gravity can not obey Lorentzsymmetry not only in its orthodoxica form but even in this new framework$f(T,\mathcal{B})$.

On existence of a possible Lorentz invariant modified gravity in Weitzenb\"{o}ck spacetime