  We show that to every local representation of the Birman-Murakami-Wenzl
algebra defined by a skew-invertible R-matrix $R\in Aut(V\otimes V)$ one can
associate pairings $V\otimes V\to C$ and $V^*\otimes V^*\to C$, where V is the
representation space. Further, we investigate conditions under which the
corresponding quantum group is of SO or Sp type.
