The formulation of the so-called homogeneous anisotropic hardening (HAH) model, which was originally proposed in Barlat et al. (2011), is refined. With the new features, this distortional plasticity-based constitutive model predicts the mechanical response of metals subjected to non-proportional loading with improved accuracy, in particular for cross-loading. In that case, applications to two different steels are provided for illustration purposes. For mild steel, the stress overshoot of the monotonic flow curve observed during a double load change is well reproduced by the model. In addition, for a dual-phase steel deformed in a two-step tension test with axes at 450 from each other, the new features allow the reloading yield stress to be lower than the unloading flow stress, in good agreement with experimental observations. (C) 2013 Elsevier Ltd. All rights reserved.