A new form of covariance modelling for Gaussian mixture models and hidden Markov models is presented. This is an extension to an efficient form of covariance modelling used in speech recognition, semi-tied co(cid:173) variance matrices. In the standard form of semi-tied covariance matrices the covariance matrix is decomposed into a highly shared decorrelating transform and a component-specific diagonal covariance matrix. The use of a factored decorrelating transform is presented in this paper. This fac(cid:173) toring effectively increases the number of possible transforms without in(cid:173) creasing the number of free parameters. Maximum likelihood estimation schemes for all the model parameters are presented including the compo(cid:173) nent/transform assignment, transform and component parameters. This new model form is evaluated on a large vocabulary speech recognition task. It is shown that using this factored form of covariance modelling reduces the word error rate.