Abstract: In this study, we propose a fast algorithm for computing radix-4 two-dimensional Fourier transform that is suitable for implementation on a parallel architecture. Our algorithm is derived in this paper from a Cooley decimation-in-time algorithm by using an appropriate indexing process. It is proved that the number of multiplications necessary to compute our proposed algorithm is significantly reduced while the number of additions remains almost identical to that of Cooley 2D FFT`s. Comparison results show the good performance of the proposed 2D FFT algorithm against the row-column FFT transform.