This work proposes a new approach to synthesize interval observers for uncertain systems. The main novelty introduced by this approach is to conceive an interval observer as a combination between a punctual observer and a set-membership characterization of the observation error. Compared with existing methods, this approach allows more flexibility for computing the observation gain matrix and so to design an interval observer with a desired convergence rate. Moreover, only the classical observability assumption is needed to apply the proposed interval observer design method. An illustrative example is presented to show the performance of this approach.