A bit level systolic array system is proposed for the Winograd Fourier transform algorithm. The design uses bit-serial arithmetic and, in common with other systolic arrays, features nearest-neighbour interconnections, regularity and high throughput. The short interconnections in this method contrast favourably with the long interconnections between butterflies required in the FFT. The structure is well suited to VLSI implementations. It is demonstrated how long transforms can be implemented with components designed to perform a short length transform. These components build into longer transforms preserving the regularity and structure of the short length transform design.