•Homogeneous anisotropic hardening (HAH) model formulation improved.•Low cross-loading yield stress now captured by HAH model.•Latent hardening formulation enhanced to better reflect experimental results.•No singularity anymore in evolution rate of microstructure deviator. 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 45° 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.