  For a C$^{*}$-bialgebra $A$ with a comultiplication $\Delta$, a universal
$R$-matrix of $(A,\Delta)$ is defined as a unitary element in the multiplier
algebra $M(A\otimes A)$ of $A\otimes A$ which is an intertwiner between
$\Delta$ and its opposite comultiplication $\Delta^{op}$. We show that there
exists no universal $R$-matrix for some C$^{*}$-bialgebras.
