An algebraic method based on unknown input observer for fault estimation in linear time invariant system with unknown input is implementable if matching condition is satisfied. Matching condition limits practical application of these methods. In this article, a method is proposed for fault estimation which need not to satisfy matching condition. Unlike classical methods, the provided method doesn’t require for auxiliary output for fault estimation. In first step, the unknown input is divided in two parts: the matched and the unmatched unknown inputs. Assuming that there exist a dynamic model for the unmatched part, new augmented system is constructed. The augmented system has revealed as a new system with matched unknown input. Then, the effect of matched unknown input has perfectly removed from observer estimation using the traditional unknown input decoupling strategy. In next step, the full order observer is designed for the augmented system. A fast adaptive law is employed for the fault estimation. Lyapunov stability condition of state and fault estimation is derived by linear matrix inequality(LMI) criteria. The effectiveness of the proposed method is shown via numerical simulation on a flexible joint example.