A rotationally resolved zero-kinetic-energy (ZEKE) photoelectron spectrum has been recorded for the lowest energy valence band of H-2. A coherent laser-based extreme ultraviolet (XUV) source, tuned from 128 200-128 900 cm-1 excites the molecules to the ionization limit, and near-threshold electrons, in a narrow energy bandwidth (a few cm-1) just below the ionization limit, are detected by field ionization as a function of laser wavelength. The rotational components for the H-2+X (2)SIGMA(g)+-H-2 X(1)SIGMA(g)+ (2-0) vibrational band show different relative intensities, compared to the conventional photoelectron spectrum and to the predictions of theoretical calculations. The perturbed intensities of the N+ = 0 <-- J" = 0 and the 0 <-- 2 rotational lines are shown to be attributable to an interaction of the pseudocontinuum of near-threshold N+ = 0 np J' = 1 Rydberg states, with the interloper N+ = 2, 26p J' = 1 state. The enhanced intensity of the 2 <-- 0 rotational line is attributable to a "complex resonance" involving the upsilon+ = 3 R(0) 8p0 transition.