This note is concerned with the observer design for linear systems with unknown inputs. An equivalent system, which is free of unknown inputs, is derived for the purpose of the observer design. Based on the equivalent system description, one can design an observer (full order, reduced order, minimal order or functional) for linear systems with unknown inputs using well-known techniques. It is shown that the equivalent system exists as long as there exists a disturbance decoupled observer. Two sets of the known existence conditions of disturbance decoupled observers are proved to be equivalent.