We report the discovery ($20sigma$) of kilohertz quasi-periodic oscillations (kHz QPOs) at ~ 690 Hz from the transient neutron star low-mass X-ray binary EXO 1745-248. We find that this is a lower kHz QPO, and systematically study the time variation of its properties using smaller data segments with and without the shift-and-add technique. The quality (Q) factor occasionally significantly varies within short ranges of frequency and time. A high Q-factor (264.5 +- 38.5) of the QPO is found for a 200 s time segment, which might be the largest value reported in the literature. We argue that an effective way to rule out kHz QPO models is to observationally find such high Q-factors, even for a short duration, as many models cannot explain a high coherence. However, as we demonstrate, the shift-and-add technique cannot find a very high Q-factor which appears for a short period of time. This shows that the coherences of kHz QPOs can be higher than the already high values reported using this technique, implying further constraints on models. We also discuss the energy dependence of fractional rms amplitude and Q-factor of the kHz QPO.
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