Let \(\cal{A}\) be an arbitrary hereditary abelian category. Lu and Peng (2021) defined the semi-derived Ringel-Hall algebra \(\mathbf{SDH}(\cal{A})\) of \(\cal{A}\) and proved that \(\mathbf{SDH}(\cal{A})\) has a natural basis and is isomorphic to the Drinfeld double Ringel-Hall algebra of \(\cal{A}\) . In this paper, we introduce a coproduct formula on \(\mathbf{SDH}(\cal{A})\) with respect to the basis of \(\mathbf{SDH}(\cal{A})\) and prove that this coproduct is compatible with the product of \(\mathbf{SDH}(\cal{A})\) , and thereby the semi-derived Ringel-Hall algebra of \(\cal{A}\) is endowed with a bialgebra structure which is identified with the bialgebra structure of the Drinfeld double Ringel-Hall algebra of \(\cal{A}\) .
