We introduce a new sampling strategy for the two-parameter Poisson-Dirichlet process mixture model, also known as Pitman-Yor process mixture model (PYM). Our sampler is therefore applicable to the well- known Dirichlet process mixture model (DPM). Inference in DPM and PYM is usually performed via Markov Chain Monte Carlo (MCMC) methods, specifi cally Gibbs sampler. These sampling methods are usually divided in two classes: marginal and conditional algorithms. Each method has its merits and limitations. The aim of this paper is to propose a new sampler which combines the main advantages of each class. Our method relies on a result of [Pit96b] for updating Pitman-Yor processes. The in finite part of the unconditional process is sampled in two ways, leading to two variants of the proposed sampler. We also propose a threshold to improve mixing in the first variant of our algorithm. The two variants of our sampler are compared with a marginal method (algorithm 8 of [Nea00]) and two state of the art conditional algorithms which are formulated in the space of cluster labels namely the efficient slice sampler of [KGW11] and the truncated blocked Gibbs sampler of [IJ01]. We also investigate effects of removing the proposed threshold in the first variant of our algorithm and introducing the threshold in the efficient slice sampler of [KGW11]. Results on real and simulated data sets illustrate that our algorithms outperform the other conditionals in terms of mixing properties.