  In this paper, we study the general form of three-point functions of
conserved current multiplets $S_{\alpha(k)}= S_{(\alpha_1 \dots \alpha_k)}$ of
arbitrary rank in four-dimensional ${\mathcal N}=1$ superconformal theory. We
find that the correlation function of three such operators $\langle
\bar{S}_{\dot{\alpha}(k)} (z_1) S_{\beta(k+l)} (z_2) \bar{S}_{\dot{\gamma}(l)}
(z_3) \rangle$ is fixed by the superconformal symmetry up to a single complex
coefficient though the precise form of the correlator depends on the values of
$k$ and $l$. In addition, we present the general structure of mixed correlators
of the form $\langle \bar{S}_{\dot{\alpha}(k)} (z_1) S_{\alpha(k)} (z_2) L(z_3)
\rangle$ and $\langle \bar{S}_{\dot{\alpha}(k)} (z_1) S_{\alpha(k)} (z_2)
J_{\gamma \dot{\gamma}} (z_3) \rangle$, where $L$ is the flavour current
multiplet and $J_{\gamma \dot{\gamma}}$ is the supercurrent.
