This paper presents a novel structure for constructing two-channel quincunx quadrature mirror filter (QQMF) banks. The analysis and synthesis filters of the QQMF bank are composed of two-dimensional (2-D) recursive digital allpass filters with symmetric half-plane support regions. Using the 2-D doubly complementary half-band property possessed by the analysis and synthesis filters, we facilitate the design of the digital allpass-based two-channel QQMF banks. For finding the coefficients of the 2-D recursive symmetric half-plane digital allpass filters, the design problem is appropriately formulated to result in an optimization problem that can be solved by using a weighted least-squares algorithm in the minimax (L∞) optimal sense. The novelty of the proposed design method is that the designed 2-D QQMF bank achieves perfect magnitude response and possesses satisfactory phase response without requiring extra phase equalizer. Simulation results are also provided for illustration and comparison. Copyright © 2012 John Wiley & Sons, Ltd.