A new nonlinear coarse-mesh rebalance (CMR) method is developed and tested to accelerate the one- and two-dimensional discrete ordinates neutron transport calculations. The method is based on rebalance factors that are angular dependent and defined on the coarse-mesh boundaries only. Unlike the conventional CMR method that is only conditionally stable, Fourier analysis and numerical tests show that this coarse-mesh angular dependent rebalance (CMADR) method is unconditionally stable for any optical thickness, scattering ratio, and coarseness and that the acceleration is very effective in most cases.