  Let $G$ be a reductive group over a local field $F$ satisfying the
assumptions of \cite{Deb1}, $G_{reg}\subset G$ the subset of regular elements.
Let $T\subset G$ be a maximal torus. We write $T_{reg}=T\cap G_{reg}$. Let $dg
,dt$ be Haar measures on $G$ and $T$. They define an invariant measure $dg/dt$
on $G/T$. Let $\mathcal{H}$ be the space of complex valued locally constant
functions on $G$ with compact support. For any $f\in \mathcal{H} ,t\in T_{reg}$
we define $I_t(f)=\int_{G/T}f(\bar gt\bar g^{-1})dg/dt$. Let $P$ be the set of
conjugacy classes of unipotent elements in $G$. For any $\Omega \in P$ we fix
an invariant measure $\omega$ on $\Omega$. As well known \cite {R} for any
$f\in \mathcal{H}$ the integral $$I_\Omega (f)=\int_\Omega f\omega$$ is
absolutely convergent. Shalika \cite{Sh} has shown that there exist functions
$\tilde{j}_\Omega (t),\Omega \in P$ on $T\cap G_{reg}$ such that $$I_t(f) =
\sum_{\Omega \in P} \tilde{j}_\Omega(t) I_\Omega(f)\qquad\qquad (\star)$$ for
any $f\in \mathcal{H} ,t\in T$ {\it near} to $e$ where the notion of {\it near}
depends on $f$. For any positive real number $r$ one defines an open
$Ad$-invariant subset $G_r$ of $G$ and a subspace $\mathcal{H}_r$ as in
\cite{Deb1}. In this paper I show that for any $f\in \mathcal{H}_r$ the
equality $(\star)$ is true for all $t\in T_{reg}\cap G_r$.
