  We study the class $Erg^\perp$ of automorphisms which are disjoint with all
ergodic systems. We prove that the identities are the only multipliers of
$Erg^\perp,$ that is, each automorphism whose every joining with an element of
$Erg^{\perp}$ yields a system which is again an element of $Erg^{\perp}$, must
be an identity. Despite this fact, we show that $Erg^\perp$ is closed by taking
Cartesian products. Finally, we prove that there are non-identity elements in
$Erg^\perp$ whose self-joinings always yield elements in $Erg^\perp$. This
shows that there are non-trivial characteristic classes included in
$Erg^\perp$.
