This brief presents a new -parallel radix-2 memory-based fast Fourier transform (FFT) architecture. The aim of this brief is to reduce the number of multiplexers and achieve an efficient memory usage. One advantage of the proposed architecture is that it only needs permutation circuits after the memories, which reduces the multiplexer usage to only one multiplexer per parallel branch. Another advantage is that the architecture calculates the same permutation based on the perfect shuffle at each iteration. Thus, the shuffling circuits do not need to be configured for different iterations. In fact, all the memories require the same read and write addresses, which simplifies the control even further and allows to merge the memories. Along with the hardware efficiency, conflict-free memory access is fulfilled by a circular counter. The FFT has been implemented on a field programmable gate array. Compared to previous approaches, the proposed architecture has the least number of multiplexers and achieves very low area usage.