The mean residual life of a life distribution, X, with a finite mean is defined by M(t) = E[X - t|X > t] for t > 0. Kochar etal. (2000) provided an estimator of M when it is assumed to be decreasing. They showed that its asymptotic distribution was the same as that of the empirical estimate, but only under very stringent analytic and distributional assumptions. We provide a more general asymptotic theory, and under much weaker conditions. We also provide improved asymptotic confidence bands.