In this paper, we give a new observer design methodology for single-output uniformly observable systems. In fact, the proposed observer is an improvement of the high gain observer given by Gauthier et al. (1992). The improvement lies basically in the fact that part of the non-linearity of the system is incorporated in the observer design strategy. Consequently, unlike the observer given in Gauthier et al. (1992), the gain of the improved observer is function of the state estimate. A comparison of the proposed observer to that given by Gauthier et al. (1992), is made via a simulation example dealing with a flexible joint mechanism and it is shown that the improved observer is more robust with regard to measurement noise and present less transient oscillations. An extension of the design strategy is also presented for a more general class of non-linear systems.