Susceptibility Tensor Imaging (STI) is a recently developed technique that uses phase data to solve for the underlying susceptibility tensor of the tissue. While STI has the potential for early diagnosis of many diseases including Parkinson’s and Alzheimer’s, it suffers from low image quality. From physics, the susceptibility tensor can be shown to be symmetric, so current approaches impose a symmetry constraint during inversion. We propose an inversion algorithm without this constraint, and instead enforce symmetry post-inversion by decomposing the result into symmetric and antisymmetric parts. We justify this approach empirically by comparing reconstructions of mouse brain and kidney data.