The ATLAS \(b\)-jet trigger system is crucial as it is important to be able to efficiently select events containing \(b\)-jet at the trigger level for analyses that involve many \(b\)-quarks in the final states, such as the search for \(HH \rightarrow 4b\) production. However, in Run-2 the ATLAS \(b\)-tagger did not distinguish between jets containing a single \(b\)-hadron (\(b\)-jets) and jets containing 2 \(b\)-hadrons (\(bb\)-jet). Collision events involving small-angle \(g \rightarrow b\bar{b}\) splitting, resulting in \(bb\)-jet are common in the LHC. Rejecting them in real-time would significantly reduce the readout rates of multi-b-jet triggers and ensure efficient signal extraction, which is particularly important for analyses that use multi-\(b\)-jet trigger chains. The proposed poster shows an approach to reject \(bb\)-jets in the ATLAS online \(b\)-taggers, the proposed implementation and the implications for the ATLAS Run-3 physics programme.