  A new four-dimensional family of skew-symmetric solutions of the Jacobi
equations for Poisson structures is characterized. As a consequence, previously
known types of Poisson structures found in a diversity of physical situations
appear to be obtainable as particular cases of the new family of solutions.
Additionally, it is possible to apply constructive methods for the explicit
determination of fundamental properties of those solutions, such as their
Casimir invariants, symplectic structure and the algorithm for the reduction to
the Darboux canonical form, which have been reported only for a limited sample
of known finite-dimensional Poisson structures. Moreover, the results developed
are valid globally in phase space, thus ameliorating the usual scope of Darboux
theorem which is of local nature.
