  We consider the dyadic paraproducts $\pi_\f$ on $\T$ associated with an
$\M$-valued function $\f.$ Here $\T$ is the unit circle and $\M$ is a tracial
von Neumann algebra. We prove that their boundedness on $L^p(\T,L^p(\M))$ for
some $1<p<\infty $ implies their boundedness on $L^p(\T,L^p(\M))$ for all
$1<p<\infty$ provided $\f$ is in an operator-valued BMO space. We also consider
a modified version of dyadic paraproducts and their boundedness on
$L^p(\T,L^p(\M)).
