In this note we present a high-gain observer for nonlinear uniformly observable SISO systems for which the high-gain parameter is determined adaptively on-line. The adaptation scheme is simple and universal in the sense that it is independent of the system the observer is designed for. Unlike in an earlier approach, the gain is adapted continuously in the present paper. This further simplifies the adaptation law and also leads to lower values of the high-gain parameter. We prove that the observer output error becomes smaller than a User specified bound for large times and that the adaptation converges.