We present a new technique for accurately determining the ages of starbursts in post-starburst galaxies. In particular, it uses the strength of the Ca II H + H$��$ absorption feature relative to that of Ca II K to separate the effects of burst strength from burst age in a spectrum comprised of a post-starburst population and an underlying old galaxy population. To test the technique we have measured spectral indices in the observed spectra of three post-starburst early-type galaxies. The three galaxies are shown to have different post-starburst ages, ranging from 0 Gyr to 1.5 Gyr after completion of the burst. We also demonstrate that if the burst contributes greater than 50\% of the light at 4000 ��\ then the technique can distinguish between a post-starburst systems and models in which a constant star formation history is suddenly truncated, such as that which could occur in a spiral that is rapidly stripped of its interstellar medium. Finally, we demonstrate that while the technique is well-suited for determining the time elapsed since the termination of a starburst (up until 2 Gyr after the end of the burst), the derived termination times are relatively insensitive to the duration of the burst.

14 pages + 7 figures, uuencoded gzipped postscript. To appear in January AJ