High-gain observers proved to be a useful tool in the design of output feedback control of nonlinear systems. However, the observer faces a numerical challenge when its dimension is high. For an observer of dimension rho and a high-gain parameter k, the observer gain is of the order of k(rho) and the observer variables could be of the order of k(rho-1) during the transient period. This paper presents a new high-gain observer that is based on cascading lower-dimensional observers with saturation functions in between them. The observer gain in the new observer is of the order of k and its variables are limited to be of the order of k during the transient period. It is shown that the cascade observer has properties similar to the standard one. In particular, a nonlinear separation principle is proved. (C) 2017 Elsevier Ltd. All rights reserved.