In multitarget tracking, many particle approximations are available to sample from the filtering density, with the effect that multitarget particles are obtained by discarding or replicating globally the existing multitarget particles, i.e. the particles for all the different targets are replicated from the same multitarget particle. A better design would be to produce shuffled multitarget particles such that the particle for each different target can be replicated from a different multitarget particle. An efficient solution has been proposed by Ubéda-Medina et al. under a posterior independence assumption that is almost never met in practical situations. The objective of this work is to propose another solution that does not rely on the posterior independence assumption. This new solution is based on introducing an auxiliary Markov transition, and is seen as an extension of the auxiliary particle filter.