We investigated the effect of the astigmatic phase on the intensity distribution of coherent nonsingular beams during propagation. Compared with the conventional twisted beam, a beam carrying the astigmatic phase could be easily generated and operated by the phase hologram in experiment. It is found that rotating the hologram could change the rotation angle and direction of the intensity distribution. The speed of rotation is also affected by the twist strength coefficient. However, rotation does not occur in some special cases. By analyzing the simulation and experimental results, we proposed a symmetric transformation to explain the phenomenon we observed. The effect of the astigmatic phase is described as flipping the intensity distribution, where the direction of the symmetric axis is controlled by the rotation angle of the phase hologram. Whether rotation occurs depends on the symmetry of the intensity distribution along the symmetric axis in the initial in-plane. Meanwhile, the twist strength coefficient could control the rate of the symmetric transformation process and the divergence angle of the beam. The new interpretation might help to inspire the investigation of other types of astigmatic beams. Our research has some application prospects in the field of beam control and transmission, especially for scenes where a special intensity distribution of the beam is needed at a certain distance.