The GARCH-t model is widely used to predict volatilty. However, modeling the conditional variance as a linear combination of past squared observations may not be the best approach if the standardized observations are non-Gaussian. A simple modi.cation lets the conditional variance, or its logarithm, depend on past values of the score of a t-distribution. The fact that the transformed variable has a beta distribution makes it possible to derive the properties of the resulting models. A practical consequence is that the conditional variance is more resistant to extreme observations. Extensions to deal with leverage and more than one component are discussed, as are the implications of distributions other than Student's t.