We have analyzed seventeen observations of the low-mass X-ray binary and atoll source 4U 1728–34 , carried out by the Rossi X-ray Timing Explorer in 1996 and 1997 . We obtain precise measurements of the frequencies of the two simultaneous kilohertz quasi-periodic oscillations ( kHz QPOs ) in this source . We show that the frequency separation between the two QPO , \Delta \nu , is always significantly smaller than the frequency of the nearly-coherent oscillations seen in this source during X-ray bursts , even at the lowest inferred mass accretion rate , when \Delta \nu seems to reach its maximum value . We also find that \Delta \nu decreases significantly , from 349.3 \pm 1.7 Hz to 278.7 \pm 11.6 Hz , as the frequency of the lower frequency kHz QPO increases from 615 to 895 Hz . This is the first time that variations of the kHz QPO peak separation are measured in a source which shows nearly-coherent oscillations during bursts .