From observation and experience, earthquake recurrence induced by the same fault should be influenced by "memory", or such a stochastic process should be non-stationary rather than being stationary. For instance, the same fault triggering the recent Tohoku earthquake in Japan is less likely to trigger another one in the coming few years, but the probability will be increasing with time. However, the commonly used Poisson process considers the earthquake as a stationary stochastic process, resulting in the identical probability regardless whether the next earthquake occurs in 2020∼2030 or 2220∼2230. As a result, based on the mechanism of faulting, this paper introduces a new analytical model to properly take the earthquake memory effect into account. A case study in Central Taiwan is given, which is considered to provide a more realistic result compared to that from the stationary stochastic process suggested by Poisson model.