  Let $\mathbb S$ be a Clifford module for the complexified Clifford algebra
$C\ell(\mathbb R^n)$, $\mathbb S'$ its dual, $\rho$ and $\rho'$ be the
corresponding representations of the spin group $Spin(\mathbb R^n)$. The group
$G=Spin(\mathbb R^{1,n+1})$ is the (twofold covering) of the conformal group of
$\mathbb R^n$. For $\lambda, \mu\in \mathbb C$, let $\pi_{\rho, \lambda}$
(resp. $\pi_{\rho',\mu}$) be the spinorial representation of $G$ on $ \mathbb
S$-valued $\lambda$-densities (resp. $\mathbb S'$-valued $\mu$-densities) on
$\mathbb R^n$. For $0\leq k\leq n$ and $m\in \mathbb N$, we construct a
symmetry breaking differential operator $B_{k;\lambda,\mu}^{(m)}$ from
$C^\infty(\mathbb R^n \times \mathbb R^n, \mathbb S\otimes \mathbb S')$ into
$C^\infty(\mathbb R^n, \Lambda^*_k(\mathbb R^n))$ which intertwines the
representations $\pi_{\rho, \lambda}\otimes \pi_{\rho',\mu} $ and
$\pi_{\tau^*_k,\lambda+\mu+2m}$, where $\tau^*_k$ is the representation of
$Spin(\mathbb R^n)$ on $\Lambda^*_k(\mathbb R^n)$.
