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