Abstract. Computation of homology or cohomology is intrinsically a problem of high combinatorial complexity. Recently we proposed a new efficient algorithm for computing cohomologies of Lie algebras and superalgebras. This algorithm is based on partition of the full cochain complex into minimal subcomplexes. The algorithm was implemented as a C program LieCohomology. In this paper we present results of applying the program LieCohomology to the algebra of hamiltonian vector fields $\mathrm{H}(2|0)$. We demonstrate that the new approach is much more efficient comparing with the straightforward one. In particular, our computation reveals some new cohomological classes for the algebra $\mathrm{H}(2|0)$ (and also for the Poisson algebra $\mathrm{Po}(2|0)$).