Due to their well-known indeterminacies, factor models require identifying assumptions to guarantee unique parameter estimates. For Bayesian estimation, these identifying assumptions are usually implemented by imposing constraints on certain model parameters. This strategy, however, may result in posterior distributions with shapes that depend on the ordering of cross-sections in the data set. We propose an alternative approach, which relies on a sampler without the usual identifying constraints. Identification is reached ex-post based on a Procrustes transformation. Resulting posterior estimates are ordering invariant and show favorable properties with respect to convergence and statistical as well as numerical accuracy.