The long-range tilt orientational order in L-beta,gamma-dimyristoyl-alpha-phosphatidyl-ethanolamine (DMPE) monolayers is visualized using Brewster angle microscopy. Compact condensed phase domains in DMPE monolayers exhibit an inner structure of segments distinguished by their different reflectivity due to a different azimuthal orientation of the molecules. The azimuthal molecular orientation jumps at the boundaries of each segment. The inner structure of domains can be understood analogously to the star textural defect in thin liquid-crystal films. The orientational order in DMPE monolayers is lower than in monolayers of other amphiphiles showing similar segment structures indicated mainly by the occurrence of segment structures with varying number of segments. The segment boundaries are wound and the orientation changes continuously within each segment. The same sense of bowing in all domains reflects the chirality of the molecule.