A new concept of the unknown input observability, namely(r, s ; K)observability, for discrete-time linear multivariable systems is introduced. This concept is an extension of the conventional unknown input observability and reconstructibility. Necessary and sufficient conditions for the(r, s ; K)observability of the given system are derived by introducing a new unobservable subspace and presenting algorithms for obtaining the subspace. It is also shown that these new concepts are closely related to the existence condition of a dead-beat observer for a decentralized control system.