The aim of this paper is to construct an observer for linear multivariable systems with unknown inputs by using the following result: a full order observer converges to a reduced order observer as some poles approach infinity in the left half complex plane. We show that this observer is equivalent to the perfect observer, and investigate a condition to construct it without the divergence of the initial estimation errors. This construction method allows us to clarify the degree of freedom in assigning the eigenvalues and eigenvectors of the unknown input observer.