Annth-order closed-loop discrete-time system is said to exhibit a deadbeat response if any arbitrary initial state is taken to the origin innsteps. This paper studies the problem of obtaining a deadbeat response for a discrete-time system by means of constant output feedback and establishes the condition for the existence of a dead-beat controller. This condition is obtained directly from the restrictions on attainable poles when constant output feedback is employed. When the condition is satisfied, the required output feedback matrix exists and is calculated from a relationship given in the paper. The problem is first solved for single-input systems and the result is then extended to multivariable systems, where the output feedback matrices used are restricted to having unity rank. Deadbeat control of multivariable systems by means of unrestricted output feedback matrices is also discussed. A number of illustrative numerical examples are given.