  A Clifford algebra Cl(V,\eta\in V^*\otimes V^*) jointly with a Clifford
cogebra Cl(V,\xi\in V\otimes V) is said to be a Clifford biconvolution
Cl(\eta,\xi). We show that a Clifford biconvolution for dim_R Cl=4 does possess
an antipode iff det(id-\xi\circ\eta)\neq 0. An antipodal Clifford biconvolution
is said to be a Clifford Hopf gebra. We study the Clifford Hopf gebra and
examples of antipode less Clifford bigebras including the Grassmann case.
