Let H be a Hopf algebra, B a bialgebra, and ( B, ◃, ρ) a right H-Hopf module. Assume that ( B, ρ) is a right H-comodule algebra, ( B, ◃) is a right H-module coalgebra, and let A = B = { a ∈ B | ρ( a) = a ⊗ 1}. Then we prove that B has a factorization of A□ (the underlying space is A ⊗ H) as a bialgebra, which generalizes Radford's factorization of bialgebras with projection [12].