The design of a two-channel nonuniform-division filter (NDF) bank with infinite impulse response (IIR) analysis/synthesis filters and low group delay in the sense of L1 error criteria is considered. The problem formulation results in a nonlinear optimisation problem. Based on a variant of Karmarkar's algorithm, the optimisation problem is solved through a frequency sampling and iterative approximation technique to find the tap coefficients and the reflection coefficients for the numerator and the denominator of the IIR analysis filters. An efficient stabilisation procedure ensures that the reflection coefficients lie in (-1, 1). Simulation results are provided for illustration and comparison.