Quasicrystalline precipitates in ZrAlNiCuNb alloy were systematically studied by transmission electron microscopy. It was found that precipitates always contain various linear phason strains. By electron diffraction analysis, two types of linear phason strain with two different directions perpendicular to the incident beam described by strain matrices with only one nonzero element were identified. After measuring the deviations of diffraction spots and quantitatively fitting against their perpendicular components of the reciprocal lattice vectors, the phason strain matrices were obtained. Domain structures formed as a result of linear phason strain variants along directions with equal probability. Electron diffraction and high-resolution electron imaging provide supportive evidence of this result.