We present a nonperturbative quantum study of high-order above-threshold detachment of H⁻ in intense laser fields using an accurate one-electron model potential and a new time-dependent non-Hermitian Floquet approach. Detailed exploration of the electron energy and angular distributions is pursued for the laser field intensities 10¹⁰–10¹¹ W cm⁻² and wavelength 10.6 µm. In accordance with semiclassical predictions, the electron energy spectrum exhibits a plateau region in the higher energy part. Transformation of the electron angular distributions in the plateau region is discussed. The computational method involves the complex-scaling generalized pseudospectral (CSGPS) spatial discretization of the Hamiltonian and non-Hermitian time propagation of the time-evolution operator by means of the split-operator technique in the energy representation. The approach is designed for effective treatment of multiphoton processes in very intense and/or low-frequency laser fields, which are generally more difficult to treat using the conventional time-independent Floquet matrix techniques.