  Let $g$ be a complex semisimple Lie algebra with adjoint group $G$. Suppose
that $\sigma$ is an involutive automorphism of $g$. Then $\sigma$ induces
uniquely an involution of $G$ also denoted by $\sigma$, let $K=G^\sigma$ be a
subgroup of $\sigma$-fixed points. Consider a direct decomposition $g=k+p$ of
$g$ into eigenspaces for $\sigma$. Then $p$ is a $K$-module. Denote by
$a\subset p$ any maximal abelian ad-diagonalizable subalgebra. Consider the
``baby Weyl group'' $W=N_K(a)/Z_K(a)$. Let $\psi: C[p]^K\to C[a]^W$ be a
restriction map of algebras of invariants. Then the famous Chevalley
restriction theorem states that $\psi$ is an isomorphism. The aim of this paper
is prove the following Theorem. The restriction map $\psi: C[p\times p]^K\to
C[a\times a]^W$ is surjective.
