Magnetic domain wall structures in an Fe (110) monolayer are determined by the highly precise first principles full-potential linearized augmented plane-wave method including intra-atomic noncollinear magnetism. The self-consistent results demonstrate that the magnetization changes from one orientation to the opposite (180 degrees ) orientation within an 8 A width without any abrupt rotation. This narrow domain wall is found to arise from band effects. Our results are consistent with and support domain walls having a 6 A width recently observed in spin-polarized scanning tunneling microscopy experiments.