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This paper deals with the design of full order observers for linear systems with unknown inputs. Two different approaches are developed using straightforward matrix operations and providing practical design. Specially, it is noted that when no mention is made on the existence conditions by the first approach [F. Yang et al., 1988], the existence conditions are well formulated by the second one [M. Darouach et al., 1994]. Furthermore, the developments are simple and direct compared to other approaches given in the literature. Design, advantages and drawbacks of the two approaches are illustrated by the same numerical example.