  We show that (central) Cowling-Haagerup constant of discrete quantum groups
is multiplicative, which extends the result of Freslon to general (not
necesarilly unimodular) discrete quantum groups. The crucial feature of our
approach is considering algebras $\mathrm{C}(\mathbb{G}),
\operatorname{L}^{\infty}(\mathbb{G})$ as operator modules over
$\operatorname{L}^1(\mathbb{G})$.
