This paper presents a new four-dimensional (4D) lattice structured digital filter, having a minimal number of delay elements. This filter, besides having a minimal number of delay elements, also has an absolutely minimal state-space vector. The new finite impulse response (FIR) digital filter is characterized by a lattice structure having alternate delay element orientation. Furthermore, the transfer function coefficients of the proposed 4D filter are complements of the conventional lattice filters. The results of this paper are directly applicable to one-dimensional (1D) lattice digital filters. 4D and two-dimensional (2D) low-order examples are provided to show the features of the circuit and state-space realization structures.