The second order Ces\`aro sequence spaces of non-absolute type $X_p(\Delta^2)$ for $1\leq p\leq\infty$ were defined and studied in [1]. It seems, however, that the characterizations of their $\beta$-duals given there do not hold for $1<p\leq\infty$. In this paper, we determine the $\beta$-duals $(X_p(\Delta^2))^\beta$ for $1\leq p\leq\infty$.