Relative partial photoionization cross sections and angular distribution parameters beta have been measured for the first and fourth (5p)(-1) photoelectron (PE) bands of atomic iodine by performing angle-resolved constant-ionic-state (CIS) measurements on these PE bands between the (1)D(2) and (1)S(0) (5p)(-1) ionic thresholds in the photon energy region of 12.9-14.1 eV. Rydberg series arising from the 5p-->ns and 5p-->nd excitations are observed in both the first PE band, I(+)((3)P(2))<--I((2)P(3/2)), and the fourth PE band, I(+)((1)D(2))<--I((2)P(3/2)), CIS spectra. For each Rydberg state, the resonance energy, quantum defect, linewidth, line shape, and photoelectron angular distribution parameter beta have been determined. For the beta-plots for each PE band, only resonances corresponding to 5p-->nd excitations are observed; no resonances were seen at photon energies corresponding to the 5p-->ns resonances in the CIS spectra. The beta-plots are interpreted in terms of the parity unfavored channel with j(t)=4 being the major contributor at the 5p-->nd resonance positions, where j(t) is the quantum number for angular momentum transferred between the molecule, and the ion and photoelectron. Comparison of the results obtained with those published for bromine shows reasonably good agreement for the CIS spectra but poor agreement for the beta-plots. It appears that parity unfavored channels are playing a greater role in the valence (np)(-1) ionization of atomic iodine than in the corresponding ionization of atomic bromine.