This paper proposes an improved prediction update for extended target tracking with the random matrix model. A key innovation is to employ a generalised non-central inverse Wishart distribution to model the state transition density of the target extent; resulting in a prediction update that accounts for kinematic state dependent transformations. Moreover, the proposed prediction update offers an additional tuning parameter c.f. previous works, requires only a single Kullback-Leibler divergence minimisation, and improves overall target tracking performance when compared to state-of-the-art alternatives.