General form of the *-product on the Grassmann algebra

We study the general form of the noncommutative associative product (the *- product) on the Grassmann algebra; the *-product is treated as a deformatio n of the usual "pointwise" product. We show that zip to a similarity transf ormation, there exists only one such product. We discuss the relation of th e algebra F (the algebra of the elements of the Grassmann algebra with the *-product as a product) to the Clifford algebra.