A measure of temporal predictability is defined, and used to separate linear mixtures of signals. Given any set of statistically independent source signals, it is conjectured here that a linear mixture of those signals has the following property: the temporal predictability of any signal mixture is less than (or equal to) that of any of its component source signals. It is shown that this property can be used to recover source signals from a set of linear mixtures of those signals by finding an un-mixing matrix which maximises a measure of temporal predictability for each recovered signal. This matrix is obtained as the solution to a generalised eigenvalue problem; such problems have scaling characteristics of O(N^3), where N is the number of signal mixtures. In contrast to independent component analysis, the temporal predictability method requires minimal assumptions regarding the probability density functions of source signals. It is demonstrated that the method can separate signal mixtures in which each mixture is a linear combination of source signals with super-Gaussian, sub-Gaussian, and Gaussian probability density functions, and on mixtures of voices and music.