  Let $D$ be the set of $\beta \in (1, 2]$ such that $f_\beta$ is a symmetric
tent map with finite critical orbit. For $\beta \in D$, by operating Denjoy
like surgery on $f_{\beta}$, we constructed a $C^1$ unimodal map
$\tilde{g}_\beta$ admitting a thick hyperbolic repelling invariant Cantor set
which contains a wild Cantor attractor. The smoothness of $\tilde{g}_\beta$ is
ensured by the effective estimation of the preimages of the critical point as
well as the prescribed lengths of the inserted intervals. Furthermore, $D$ is
dense in $(1, 2]$, and $\tilde{g}_\beta$ can not be $C^{1+\alpha}$ because the
hyperbolic repelling invariant Cantor set of $C^{1+\alpha}$ map has Lebesgue
measure equal to zero.
