  Let $A$ be a Banach algebra. The flip on $A \otimes A^\op$ is defined through
$A \otimes A^\op \ni a \tensor b \mapsto b \tensor a$. If $A$ is ultraprime,
$\El(A)$, the algebra of all elementary operators on $A$, can be algebraically
identified with $A \otimes A^\op$, so that the flip is well defined on
$\El(\A)$. We show that the flip on $\El(A)$ is discontinuous if $A = K(E)$ for
a reflexive Banach space $E$ with the approximation property.
