Molecular magnetic properties, such as the magnetizability, the magnetic shielding, and the current strength, all stem from the asymmetric current density tensor. The anisotropy of that tensor, previously defined from its symmetric component only, is a scalar field expected to bear useful information on molecular structure. A more general anisotropy has here been defined, considering the full asymmetric tensor and its eigenvalues in the complex plane. Computations on a few prototypical aromatic molecules show that the anisotropy of the full tensor highlights previously missed structural features and also changes in a more regular way with bond length, as compared to the already known anisotropy of the symmetric component of the tensor.