This paper studies the design of reduced-order observers for a class of linear discrete-time Markov jump systems with unknown inputs.First, a new reduced-order observer is designed for the linear system with unknown input, and the unknown input is completely decoupled by constructing the observer gain matrix.In addition, the sufficient conditions for the existence of the observer are given in the form of linear matrix inequality, and the observer error is proved to be finite time stable, which guarantees the good transient properties of the estimation.Finally, an example verifies the effectiveness and feasibility of the proposed method.