  A normalized holomorphic family (depending on $\boldsymbol \lambda \in
\mathbb C^3$) of conformally invariant trilinear forms on the sphere is
studied. Its zero set $Z$ is described. For $\boldsymbol \lambda\notin Z$, the
multiplicity of the space of conformally invariant trilinear forms is shown to
be 1, except perhaps for a denumerable subset.
