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The stochastic nature of public transport systems leads to headway variability and bus bunching, causing both operator and passenger cost to increase significantly. Traditional strategies to counter bus bunching, including bus-holding, stop-skipping, and bus substitution/insertion, suffer from trade-offs and shortcomings. Autonomous modular vehicle (AMV) technology provides an additional level of flexibility in bus dispatching and operations, which can offer significant benefits in mitigating bus bunching compared to strategies available with conventional buses. This paper introduces a novel alternative to stop-skipping by leveraging the new capabilities offered by AMVs (in particular, en-route coupling and decoupling of modular units). We develop a simple bus-splitting strategy that directs a modular bus to decouple into individual units when it experiences a headway longer than a given threshold. We then use a macroscopic simulation to present a proof-of-concept evaluation of the proposed modular strategy compared to a benchmark traditional stop-skipping strategy and the base (no control) case. We find that the proposed strategy outperforms the benchmark in decreasing each of the three travel time components: waiting time, in-vehicle time, and walking time (which it eliminates completely). It therefore reduces the overhead of bus bunching and thus the travel cost by more than twice as much as the benchmark for busy bus lines. Simultaneously, it also reduces headway variability to a comparable degree. Furthermore, we analyze different control thresholds for applying the proposed strategy, and show that it is most effective when applied proactively, i.e. with the control action being triggered even by small headway deviations.