The Bochner–Schoenberg–Eberlein (BSE)-property on commutative Banach algebras is a property related to multiplier algebras of Banach algebras. In this paper, we answer the problem (12) raised by Javanshiri and Nemati in [Amalgamated duplication of the Banach algebra [Formula: see text] along a [Formula: see text]-bimodule [Formula: see text], J. Algebra Appl. 17(9) (2018) 1850169-1–1850169-21]. In this paper, under certain conditions, we show that the amalgamated Banach algebra [Formula: see text] is BSE-algebra if and only if [Formula: see text] and [Formula: see text] are BSE-algebras.