Subband adaptive filtering has attracted much attention lately. In this paper, a new and improved structure and a new formulation for adapting the filter coefficients is discussed. The scheme is based on infinite impulse response (IIR) filterbanks, formed from allpass polyphase filters, which exhibit very high quality filtering compared to typical finite impulse response (FIR) implementations, have relatively low complexity, introduce a limited degree of phase distortion and have low delay. The new formulation yields improved convergence rate when LMS algorithm is used for coefficient adaptation. The scheme is tested in an acoustic echo canceller application and shown to give better convergence, lower delay, and lower computational cost than a comparable FIR subband scheme