AbstractWe fill a gap in the proofs in the previous works (Wu X, Mu, X. Int J. Robust Nonlin Control. 2020;30:3753Ű3772; Zhang Z, Lunze J, Wang L. Int J Control. 2020;93:1005‐1014; Zhang Z, Wang L. J Robust Nonlin Control. 2018;28:4175Ű4187; Dai, M‐Z, Zhang C, Leung H, Dong P, Li B. IEEE Trans Syst, Man, Cybern: Syst. doi:10.1109/TSMC.2021.3119670) for the consensus using the integral‐based event‐triggered controls. More precisely, it was inferred for a Lyapunov function that is uniformly bounded by showing that is uniformly bounded for . However, this argument may fail without further information while the boundedness of is crucially used for applying Barbalat's lemma. The consequence of Barbalat's lemma is that which corresponds to the desired consensus result. To overcome this gap, Ma and Zhao (Inform Sci. 2018;457‐458:208‐221) put an extra condition about the boundedness of measurement error functions inside the proposed integral‐based event‐triggering protocol. In this article, we propose a new integral‐based event‐triggering protocol for bipartite consensus problems of the multi‐agent systems whose dynamics are described by general linear systems without adding the uniform boundedness of measurement error functions as (Ma Y, Zhao J. Inform Sci. 2018;457‐458:208‐221) did. Via our new integral‐based integral control strategy, we prove that the system achieves the bipartite consensus in asymptotic regime, and provide a complete solution of the freeness of both chattering and genuinely Zeno behaviors. Numerical results are provided supporting the effectiveness of the proposed controller.