  For a virtual knot $K$ and an integer $r\geq 0$, the $r$-covering $K^{(r)}$
is defined by using the indices of chords on a Gauss diagram of $K$. In this
paper, we prove that for any finite set of virtual knots
$J_0,J_2,J_3,\dots,J_m$, there is a virtual knot $K$ such that $K^{(r)}=J_r$
$(r=0\mbox{ and }2\leq r\leq m)$, $K^{(1)}=K$, and otherwise $K^{(r)}=J_0$.
