A Monte Carlo method for the simulation of growth processes is presented, in which the number of particles is kept constant, regardless of whether the actual process results in a net loss (as in coagulation) or net increase (as in fragmentation) of particles. General expressions are derived for the inter-event time, number concentration, and expected average size as a function of time. The method is applied to two coagulation models, constant kernel and Brownian coagulation, and it is shown to provide an accurate description of the dynamical evolution of systems undergoing coagulation. This algorithm allows for indefinitely long simulations. The error scales as the inverse square root of the number of particles in the simulation and grows logarithmically in time.