  We study the kilohertz quasi-periodic oscillations (kHz QPOs) and the
band-limited noise (BLN) in the 0.5--16 Hz range observed simultaneously on the
horizontal branch (HB) and on the upper normal branch (NB) of the brightest
neutron star Low-mass X-ray Binary (LMXB) Scorpius X--1 with the observations
performed with the {\it Rossi X-Ray Timing Explorer (RXTE)}. We find that the
twin kHz QPO frequencies are positively correlated with the flux variations
taking place on the BLN time scales on the HB, in contrast to the
anti-correlation held on the time scale of the normal branch oscillation (NBO)
on the NB reported previously, suggesting that although they occur in sequence
along the color-color tracks, the BLN and the NBO are of different origins. We
also show the evidence that the frequency separation between the twin kHz QPOs
decreases with the flux by $2\sim~3$ Hz on the BLN time scales, which is
consistent with the trend on the longer time scale that the Z source traces the
HB. This further suggests that the flux variation associated with the BLN
originates from the mass accretion rate variation in the disk accretion flow.
We discuss the implications of these results for our understanding of the BLN.
