A fast frequency-domain IIR (infinite-impulse response) algorithm is proposed called the frequency-domain optimal block adaptive recursive algorithm (FOBAR). This is the frequency-domain implementation of the recently proposed time domain optimal block adaptive recursive algorithm (OBAR). The FOBAR requires fewer computations than the OBAR for high-order filters. Simulations are given for both real-life and synthetic signals. In particular, FOBAR was used successfully for high-order system identification, adaptive noise cancellation, and pole-zero prediction.