A new construction method of $R$-matrix is given. Let $A$ be a C$^{ *}$-bialgebra with a comultiplication $\Delta$. For two states $\omega$ and $\psi$ of $A$ which satisfy certain conditions, we construct a unitary $R$-matrix $R(\omega,\psi)$ of the C$^{ *}$-bialgebra $(A,\Delta)$ on the tensor product of GNS representation spaces associated with $\omega$ and $\psi$. The set $\{ R(\omega,\psi):\omega,\psi\}$ satisfies a kind of Yang-Baxter equation. Furthermore, we show a nontrivial example of such $R$-matrices for a non-quasi-cocommutative C$^{ *}$-bialgebra.
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