Reepresentation of $SU(2)\times SU(2)$

Question

Note that if $\Phi_i:SU(2)\to GL(V_i)$ are irreducible finite dimensional unitary representations then $\Phi_1\otimes\Phi_2:G\to GL(V_1\otimes V_2)$ is an irreducible finite dimensional representation of $SU(2)\times SU(2)$. Is any irreducible finite dimensional unitary representation of $SU(2)\times SU(2)$ is of this form?