  The Weyl integration model presented by An and Wang can be effectively used
to reduce the integration over $G$-space. In this paper, we construct an
especial Weyl integration model for KAK decomposition of Reductive Lie Group
and obtain an integration formula which implies that the integration of
$L^1$-integrable function over reductive Lie group $G$ can be carried out by
first integrating over each conjugacy class and then integrating over the set
of conjugacy classes.
