  The Gaudin model based on the sl_2-invariant r-matrix with an extra Jordanian
term depending on the spectral parameters is considered. The appropriate
creation operators defining the Bethe states of the system are constructed
through a recurrence relation. The commutation relations between the generating
function t(\lambda) of the integrals of motion and the creation operators are
calculated and therefore the algebraic Bethe Ansatz is fully implemented. The
energy spectrum as well as the corresponding Bethe equations of the system
coincide with the ones of the sl_2-invariant Gaudin model. As opposed to the
sl_2-invariant case, the operator t(\lambda) and the Gaudin Hamiltonians are
not hermitian. Finally, the inner products and norms of the Bethe states are
studied.
