  We find the Hopf algebra $U_{g,h}$ dual to the Jordanian matrix quantum group
$GL_{g,h}(2)$. As an algebra it depends only on the sum of the two parameters
and is split in two subalgebras: $U'_{g,h}$ (with three generators) and $U(Z)$
(with one generator). The subalgebra $U(Z)$ is a central Hopf subalgebra of
$U_{g,h}$. The subalgebra $U'_{g,h}$ is not a Hopf subalgebra and its coalgebra
structure depends on both parameters. We discuss also two one-parameter special
cases: $g =h$ and $g=-h$. The subalgebra $U'_{h,h}$ is a Hopf algebra and
coincides with the algebra introduced by Ohn as the dual of $SL_h(2)$. The
subalgebra $U'_{-h,h}$ is isomorphic to $U(sl(2))$ as an algebra but has a
nontrivial coalgebra structure and again is not a Hopf subalgebra of
$U_{-h,h}$.
