The general form of the star-product on the Grassman algebra

We study the general form of the noncommutative associative product (the star-product) on the Grassman algebra; the star-product is treated as a deformation of the usual "pointwise" product. We show that up to a similarity transformation, there is only one such product. The relation of the algebra ${\cal F}$, the algebra of elements of the Grassman algebra with the star-product as a product, to the Clifford algebra is discussed.