  The Poisson, contact and Nambu brackets define algebraic structures on
$C^{\infty}(M)$ satisfying the Jacobi identity or its generalization. The
automorphism groups of these brackets are the symplectic, contact and volume
preserving diffeomorphism groups. We introduce a modification of the Nambu
bracket, which defines an evolution equation generating the whole
diffeomorphism group. The relation between the modified and usual Nambu
brackets is similar to the relation between the Poisson and contact structures.
We briefly discuss the problem of quantization of the modified bracket.
