I revisit the spin modelling of a remnant black hole resulting from a merger of two black holes moving on quasi-circular orbits. On the base of the AEI formula, I provide a new model with higher-order terms predicting the final spin norm and direction. Based on a catalogue of 870 gathered numerical simulations, I perform a fit of the unconstraint coefficients for the final spin norm prediction and thereupon prove their validity. With five assumptions derived for the AEI formula the presented formula applies for generic binaries at any initial separation. The formula therefore provides information over the whole seven-dimensional parameter space spanned by the initial mass ratio q and the initial dimensionless spins 𝒂! and 𝒂! and especially in the realms of extreme initial spins enhances its predecessor. Due to the vast range of simulations a deeper analysis of the model’s goodness considering aligned and generic binaries will be presented. Furthermore, I investigate the prediction model for the final spin direction that assumes the final spin to be aligned with the initial total angular momentum. As I will show, the validity of this assumption correlates with the magnitude of the projection of the initial total angular momentum on the orbital angular momentum. The improved formula is suitable to handle and can be applied i.e. for studying the cosmological evolution of supermassive black holes.