we discuss discrete symmetry of staggered-Wilson fermions. A potential problem with staggered-Wilson fermions in lattice QCD is discrete symmetry breaking. As discussed in [@Adams2; @Hoel], the discrete symmetry possessed by the original staggered fermion is broken to its subgroup both in the Adams-type and Hoelbling-type actions. We below list all the staggered discrete symmetries (shift, axis reversal, rotation and charge conjugation), and look into their status in staggered-Wilson fermions. Shift transformation is given by $$\begin{aligned}
\mathcal{S}_{\mu}:\,\,\chi_{x} \to \zeta_{\mu}(x)\chi_{x+\hat{\mu}}, \,\,\,\,
\bar{\chi}_{x} \to \zeta_{\mu}(x)\bar{\chi}_{x+\hat{\mu}},\,\,\,\,
U_{\nu,x} \to U_{\nu, x+\hat{\mu}}
\ ,
\label{shift1}\end{aligned}$$ with $\zeta_{1}(x)=(-1)^{x_{2}+x_{3}+x_{4}}$, $\zeta_{2}(x)=(-1)^{x_{3}+x_{4}}$, $\zeta_{3}(x)=(-1)^{x_{4}}$ and $\zeta_{4}(x)=1$. It is obvious that this transformation flips the sign of both flavored-mass terms. The Adams type is invariant under the two-shift subgroup as $x \to x+\hat{1}\pm\hat{\mu}$ while the Hoelbling type is invariant under four-shift subgroup as $x\to x+\hat{1}\pm\hat{2}\pm\hat{3}\pm\hat{4}$. Note that these subgroups include the doubled shift $x\to x+2\hat{\mu}$ as their subgroup. The axis reversal transformation is given by, $$\begin{aligned}
\mathcal{I}_{\mu}:\,\,\chi_{x} \to (-1)^{x_{\mu}}\chi_{Ix}, \,\,\,\,
\bar{\chi}_{x} \to (-1)^{x_{\mu}}\bar{\chi}_{Ix},\,\,\,\,
U_{\nu,x} \to U_{\nu, Ix}
\ ,
\label{axis1}\end{aligned}$$ with $I=I^{\mu}$ is the axis reversal $x_{\mu}\to -x_{\mu}$, $x_{\rho}\to x_{\rho}$, $\rho\not= \mu$. It again flips the sign of the flavored-mass terms. The staggered rotational transformation is given by $$\begin{aligned}
\mathcal{R}_{\rho\sigma}:\,\,\chi_{x} \to S_{R}(R^{-1}x)\chi_{R^{-1}x},\,\,\,\,
