  We reformulate the method recently proposed for constructing quasitriangular
Hopf algebras of the quantum-double type from the R-matrices obeying the
Yang-Baxter equations. Underlying algebraic structures of the method are
elucidated and an illustration of its facilities is given. The latter produces
an example of a new quasitriangular Hopf algebra. The corresponding universal
R-matrix is presented as a formal power series.
