In this paper we introduce the idea of improving the performance of parametric temporal-difference (TD) learning algorithms by selectively emphasizing or de-emphasizing their updates on different time steps. In particular, we show that varying the emphasis of linear TD( λ \lambda )'s updates in a particular way causes its expected update to become stable under off-policy training. The only prior model-free TD methods to achieve this with per-step computation linear in the number of function approximation parameters are the gradient-TD family of methods including TDC, GTD( λ \lambda ), and GQ( λ \lambda ). Compared to these methods, our _emphatic TD( λ \lambda )_ is simpler and easier to use; it has only one learned parameter vector and one step-size parameter. Our treatment includes general state-dependent discounting and bootstrapping functions, and a way of specifying varying degrees of interest in accurately valuing different states.