By using an adaptive algorithm, together with an additional dynamic system, this paper proposes a new approach to design of a state observer for a class of uncertain systems. We enlarge the class of linear systems from the canonical form of [1] by proposing an adaptive observer that allows unknown parameters to affect those unmeasured states. The result is based on a recent result which presents a design algorithm for an additional system to replace output derivative measurements with the additional dynamics. A numerical example illustrates the design procedure of the state observer