  We introduce a universal R matrix for the Jordanian deformation of $\U{
\sl(2)}$. Using $\Uh{\so(4)}=\Uh{\sl(2)} \oplus {\rm U}_{-h}(\sl(2))$, we
obtain the universal R matrix for $\Uh{\so(4)}$. Applying the graded
contractions on the universal R matrix of $\Uh{\so(4)}$, we show that there
exist three distinct R matrices for all of the contracted algebras. It is shown
that $\Uh{\sl(2)}$, $\Uh{\so(4)}$, and all of these contracted algebras are
triangular.
