The low-field susceptibility along the easy axis of the spin glass Fe2TiO5 exhibits a sharp cusp at Tg=48 K, whereas the susceptibility in transverse directions exhibits a broad maximum around 6 K. In all directions irreversibility appears already below Tg. Transverse irreversibility, however, is weaker by an order of magnitude than the longitudinal one. This behavior is discussed in terms of a model of a spin glass which has a weak random anisotropy in addition to a uniform easy axis.