In this note, a quasi-deadbeat property is introduced and a quasi-deadbeat minimax filter (DNIF) is proposed as a new class of filters for deterministic discrete-time state-space models. Constraints such as linearity, quasi-deadbeat property, and independence of the initial-state information will be required in advance, in addition to a new performance index of the worst-case gain between the disturbance and the current estimation error. The proposed DMF is obtained by directly minimizing the new performance index with above constraints. Finite impulse response (FIR) and infinite impulse response (1111) structures are suggested with emphasis on the FIR structure. The proposed DMF is represented first, in a standard batch form and then in an iterative form. It is shown that the DMF with FIR and IIR structures for deterministic systems are similar in form to the existing receding horizon unbiased FIR filter (RHUFF) and the Kalman filter, respectively, for stochastic systems.