An adaptive state observer is proposed for a class of overparametrized uncertain linear time-invariant systems without restrictive requirement of their representation in the observer canonical form. It evolves the method of Generalized Parameters Estimation-Based Observer design and, therefore, (i) does not require to identify Luenberger correction gain parameters, (ii) forms states using algebraic rather than differential equation. Additionally, the developed observer is applicable to systems with unknown output matrix and ensures exponential convergence of unmeasured state observation error under weak requirement of the regressor finite excitation. The effectiveness of the proposed solution is supported by simulation results.