A new method for determining magnetic anisotropy using anhysteric remanence susceptibility is described. The magnetic fabric of a collection of Trenton Limestone specimens has been determined using this method, as well as by conventional anisotropy of magnetic susceptibility. The results demonstrate the usefulness of the new method for finding the magnetic fabric of rock units such as the Trenton in which the bulk magnetic susceptibilities are low. A model is proposed to explain the observed foliated and lineated fabric as a consequence of overburden compaction and regional horizontal stresses. The original fabric is inferred to have been isotropic; the anisotropy resides in secondary magnetite of Late Paleozoic age. It is argued that the observed magnetic fabric must therefore be Alleghenian or younger in age. Our method has the potential to determine paleostress directions in carbonates elsewhere, provided our assumptions are correct.