  We introduce for any Poisson algebra a bicomplex of free Poisson modules, and
use it to show that the Poisson cohomology theory introduced in the paper "[M.
Flato, M. Gerstenhaber and A. A. Voronov, Cohomology and Deformation of Leibniz
Pairs, Lett. Math. Phys. 34 (1995) 77--90]" is given by certain derived
functor. Moreover, by constructing a long exact sequence connecting Poisson
cohomology groups and Yoneda-extension groups of certain quasi-Poisson modules,
we provide a way to compute this Poisson cohomology via the Lie algebra
cohomology and the Hochschild cohomology.
