This letter concerns both state estimation and parameters identification for linear system with unmatched unknown parts. It deals with a full order output delayed unknown inputs observer (DUIO), in which, the time delay concept is investigated to define a new augmented dynamic system including delayed state and output vectors. This estimation approach allows to recover the matching condition which can appear in the observer design problem. The resulting observer has been improved, from the restrictive decoupling condition point of view to guarantee the estimation of state and parameters with asymptotic convergence. Finally, a simulation example based on parametric identification is provided to highlight the feasibility of the suggested method.