  A weak chord index $Ind'$ is constructed for self crossing points of virtual
links. Then a new writhe polynomial $W$ of virtual links is defined by using
$Ind'$. $W$ is a generalization of writhe polynomial defined in [6]. Based on
$W$, three invariants of virtual links are constructed. These invariants can be
used to detect the non-trivialities of Kishino knot and flat Kishino knot.
