  To each complex number $\lambda$ is associated a representation $\pi_\lambda$
of the conformal group $SO_0(1,n)$ on $\mathcal C^\infty(S^{n-1})$ (spherical
principal series). For three values $\lambda_1,\lambda_2,\lambda_3$, we
construct a trilinear form on $\mathcal C^\infty(S^{n-1})\times\mathcal
C^\infty(S^{n-1})\times \mathcal C^\infty(S^{n-1})$, which is invariant by
$\pi_{\lambda_1}\otimes \pi_{\lambda_2}\otimes \pi_{\lambda_3}$. The trilinear
form, first defined for $(\lambda_1, \lambda_2,\lambda_3)$ in an open set of
$\mathbb C^3$ is extended meromorphically, with simple poles located in an
explicit family of hyperplanes. For generic values of the parameters, we prove
uniqueness of trilinear invariant forms.
