The design of reduced-order state observers for linear multivariable systems is considered. The procedure used is based on the assignment of prespecified sets of eigenvalues and associated eigenvectors to the observer model, whereby the state estimation error is effectively governed. It is shown, in particular, that the restrictions on the assignable eigenvectors are removed when the number of system outputs equals or exceeds half the number of state variables. Moreover, with the outputs in excess of half the state variables, some design parameters remain unaffected by the assignment of both sets of eigenvalues and eigenvectors. A certain part of these additional parameters can be adjusted to alleviate the impact of misalignment between the system and the observer initial states. The remaining part contributes to the identification of the observer matrices—other than the dynamical coefficient matrix. The one-to-one correspondence between the observability of the system and the eigenvalue assignability of the observer in the framework of this approach is demonstrated.