The cycle-life analysis of lithium ion batteries (LIBs) is generally performed from their brand-new state and under fixed charge/discharge (C/D) cycling conditions, especially under a constant cycle temperature. This, however, is not an adequate analysis since in real situations, an LIB is usually not in a fresh state and is cycled at an ambient temperature different from its past operating environment. To predict the remaining capacity of an aged LIB, we develop a four-parameter incremental fading model which introduces two quantities (K, Delta) related to the capacity loss rate and the increase of SEI thickness. The four parameters are constant in different temperatures and can be easily determined from a relatively small amount of cycle-life experimental data. We construct the temperature-independent K - Delta curve, which can capture the characteristic fading feature of a cycled LIB, called the fading trajectory in this study. From this curve, one can identify the current state of an aged LIB and its subsequent time evolution. This model accompanied by a simple experiment reveals that the nonlinear cycle fading of an aged LIB not only depends on its future cycling conditions, but it is also correlated with its past cycling history. (C) 2018 The Electrochemical Society.