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For the bright neutron star low-mass X-ray binary Sco X-1, we analyzed all updated frequencies of the twin kilohertz quasi-periodic oscillations (kHz QPOs), their correlations and distributions. We found that the frequency separation of the kHz QPO peaks appears not to be a constant, rather, it decreases with increasing inferred mass accretion rate. We show that the currently available data of Sco X-1 by Rossi X-ray Timing Explorer are inconsistent with the proposals of the beat model that the frequency separation is a constant. Our conclusions are consistent with those of some previous researchers and we discuss further implications for the kilohertz QPO models.