A Clifford A-algebra of a quadratic A-module (E, q) is an associative
and unital A-algebra (i.e. sheaf of A-algebras) associated with
the quadratic ShSetX-morphism q, and satisfying a certain universal
property. By introducing sheaves of sets of orthogonal bases (or simply
sheaves of orthogonal bases), we show that with every Riemannian quadratic
free A-module of finite rank, say, n, one can associate a Clifford
free A-algebra of rank 2n. This “main” result is stated in Theorem 3.2.