This paper proposes a new two dimensional (2D) 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 lattice structure having alternate delay element orientation. It is worth mentioning that the transfer function coefficients of the proposed 2D filter, are complements of the classic lattice filter. The results of this paper are directly applicable to one-dimensional (1D) lattice digital filters. First and second degree 2D examples are provided to show the features of the circuit and state-space realization structures.