We investigate shear wave splitting measurements performed on two years of data recorded at stations deployed in the TASMAL experiment, a network of 20 broadband seismological stations designed to record data on each side of the controversial Tasman Line in Australia. Whereas a subset of measurements previously performed on one year of data exhibited a curvilinear pattern similar to that of the Tasman Line, suggesting anisotropy frozen in the lithosphere, considering the whole data set drastically changes the situation: apparent isotropy in the Australian upper mantle is observed at numerous stations. This apparent isotropy together with the EW or NS orientations of the polarization plane of the fast S wave ($phi$) observed at some stations is consistent with a two-layer anisotropic system underneath the Australian continent, with a perpendicular orientation of $phi$ in each layer. From the latest tomographic results, the transition between the Precambrian western and Phanerozoic eastern Australia appears to define blocks of various thickness. Unlike the situation across the TESZ in Europe, these blocks do not seem to be correlated with a different behavior in terms of seismic anisotropy.