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Let 
$T$ be a Banach algebra homomorphism from a Banach algebra 
${\mathcal{B}}$ to a Banach algebra 
${\mathcal{A}}$ with 
$\Vert T\Vert \leq 1$. Recently, Bhatt and Dabhi [‘Arens regularity and amenability of Lau product of Banach algebras defined by a Banach algebra morphism’, Bull. Aust. Math. Soc.87 (2013), 195–206] showed that cyclic amenability of 
${\mathcal{A}}\times _{T}{\mathcal{B}}$ is stable with respect to 
$T$, for the case where 
${\mathcal{A}}$ is commutative. In this note, we address a gap in the proof of this stability result and extend it to an arbitrary Banach algebra 
${\mathcal{A}}$.
