The polarization axes of the ends of two PM fibers are aligned in an automatic fiber splicer by first making a linear alignment of the fiber ends (1, 1) using movable retainers (21) the same way as for conventional splicing. The fiber ends are rotated by rotatable fixtures (22) to capture images by a camera (9) and therefrom, in an image processing and analysis unit (15), as controlled by logical circuits (33) light contrast profiles are determined as functions of the angular position. From the light contrast profiles the polarization axes are determined and then they are aligned with each other. The images are captured of an area at and around the fiber ends as seen in an observation plane. This observation plane is taken to have such a position that the variation of the light contrast profiles is sufficiently large, this making the determination of the angular positions of the polarization axes have a sufficient accuracy, also for for example elliptical core fibers.