The event-driven acceptance rejection (AR) method is a computationally very advantageous Monte Carlo (MC) simulation technique for the solution of population balance equations (PBE) of coagulating systems. In the scope of the event-driven simulation approach, the simulation time is stepwise increased by a simulation time step tau, which is given be the simulated particle properties. Within this time step tau, exactly one coagulation event takes place. The method is therefore not applicable in situations, for which specific time points have to be reached by the simulation, or the time step has to be reset to a smaller value. We propose a methodology termed 'fractional MC step' which allows to reset the simulation time step of the AR method to any arbitrary smaller value than the one initially proposed. The proposed method is validated by simulations of coagulation for different initial conditions and comparison with results gained from the discrete sectional method. The potential increase of the stochastic noise is investigated by comparisons with the results from conventional MC simulation techniques. The advantages of a parallel implementation are briefly discussed. (C) 2018 Institution of Chemical Engineers. Published by Elsevier B.V. All rights reserved.