It is thought that one role of the basal ganglia is to constitute the neural substrate of action selection. We propose here a modification of the action selection model of the basal ganglia of (Gurney et al., 2001a,b) so as to improve its dynamical features. The dynamic behaviour of this new model is assessed by using the theoretical tool of contraction analysis. We simulate the model in the standard test defined in (Gurney et al., 2001b) and also show that it performs perfect selection when presented a thousand successive random entries. From a biomimetical point of view, our model takes into account a usually neglected projection from GPe to the striatum, which enhances its efficiency.