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

Non-existence of universal $R$-matrix for some C$^{*}$-bialgebras