The paper presents a new memory-efficient distributed arithmetic (DA) architecture for high-order FIR filters. The proposed architecture is based on a memory reduction technique for DA look-up-tables (LUTs); it requires fewer transistors for high-order filters than original LUT-based DA, DA-offset binary coding (DA-OBC), and the LUT-less DA-OBC. Recursive iteration of the memory reduction technique significantly increases the maximum number of filter order implementable on an FPGA platform by not only saving transistor counts, but also balancing hardware usage between logic element (LE) and memory. FPGA implementation results confirm that the proposed DA architecture can implement a 1024-tap FIR filter with significantly smaller area usage (<50%) than the original LUT-based DA and the LUT-less DA-OBC.