We propose a new way of extending the piecewise exponential estimator (PEXE) beyond the last observation, where the original PEXE and the Kaplan-Meier estimator (KME) of the true survival function (SF) are undefined. We propose additional exponential tail to the original PEXE so that the estimate of the true mean by our estimator, which we will call extended-PEXE (EPEXE), and the KME are equal. By simulations, with various survival functions, we have been able to show that EPEXE improves on both the original PEXE and the KME.