Sequential Monte Carlo (SMC) methods are one of the most important computational tool to deal with intractability in complex statistical models. In those techniques, the distribution of interest is approximated by a set of properly weighted samples. One problem with SMC algorithms is the weights degeneracy: either the weights have huge variability or high correlations between the particles. Updating the particles by a few MCMC steps has been suggested as an improvement in this case (the resample-move algorithm). The general setup is to first resample the particles in such a way that all particles are given equal weight. Thereafter the MCMC steps are applied in order to make the identical samples diverge. In this work we consider an alternative strategy where the order of MCMC updates and the resampling steps are switched, i.e. MCMC updates are performed first. The main advantage with such an approach is that by performing MCMC updates, the weights can be updated simultaneously, making them less variable. We illustrate through simulation studies how our methodology can give improved results for online Bayesian inference in general state space models.