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The ordered [ital p](1[times]1) monolayer phase of Bi on InAs(110) has been studied with the technique of angle-resolved ultraviolet photoemission spectroscopy. Three Bi-induced surface-state bands ([ital S][prime],[ital S][prime][prime], and [ital S][prime][prime][prime]) have been observed. Their respective band dispersions have been mapped along the high-symmetry lines of the surface Brillouin zone. The upper two bands, [ital S][prime] and [ital S][prime][prime], appear to be degenerate across most of the surface Brillouin zone except along the [bar [Gamma]]-[ital [bar X]][prime] symmetry line. The bandwidths of the Bi-induced states of Bi/InAs(110) are significantly narrower than that of Bi/GaAs(110) or Sb/GaAs(110). The polarization of these surface-state bands has been measured and compared to predictions of current theoretical models for Sb/GaAs(110).