  The angular momentum of an electron is characterized well by pseudospin with
$J=3/2$ in the presence of strong spin-orbit interactions. We study
theoretically the Josephson effect of superconductors in which such two $J=3/2$
electrons form a Cooper pair. Within even-parity symmetry class,
pseudospin-quintet pairing states with $J=2$ can exist as well as
pseudospin-singlet state with $J=0$. We focus especially on the Josephson
selection rule among these even-parity superconductors. We find that the
selection rule between quintet states is severer than that between spin-triplet
states formed by two $S=1/2$ electrons. The effects of a pseudospin-active
interface on the selection rule are discussed as well as those of odd-frequency
Cooper pairs generated by pseudospin dependent band structures.
