The Active Appearance Model (AAM) is a powerful generative method used for modelling and segmenting deformable visual objects. Linear iterative methods have proven to be an efficient alignment method for the AAM when initialisation is close to the optimum. However, current methods are plagued with the requirement to adapt these linear update models to the problem at hand when the class of visual object being modelled exhibits large variations in shape and texture. In this paper, we present a new precomputed parameter update scheme which is designed to reduce the error bound over the model parameters at every iteration. Compared to traditional update methods, our method boasts significant improvements in both convergence frequency and accuracy for complex visual objects whilst maintaining efficiency.