General form of the deformation of Poisson superbracket on (2,2)-dimensional superspace

Continuous formal deformations of the Poisson superbracket defined on compactly supported smooth functions on n-dimensional space taking values in a Grassmann algebra with m generating elements are described up to an equivalence transformation for the case n=m=2. It is shown that in this case the Poisson superalgebra has an additional deformation comparing with other superdimensions (n,m)