  We equip the tensor algebra of a vector space $U$ over the real or complex
field with an alternative product. The new product has the property that if we
specialize it to the symmetric tensor algebra becomes the circle product
introduced by Brouder while specialization to the antisymmetric algebra becomes
the circle product introduced by Rota and Stein. We prove some interesting
properties of this product analogous to the properties proved by the previous
authors. We use Hopf algebraic methods to simplify our results. Finally we
prove that the classical algebraic structure of the tensor algebra and the new
one are homomorphically isomorphic.\bigskip
