  We discovered a single kHz quasi-periodic oscillation (QPO) near 1150 Hz in
the Rossi X-ray Timing Explorer X-ray light curve of the low mass X-ray binary
and atoll source 4U 1735-44. The rms amplitude of this peak was 2-3%, and the
FWHM 6-40 Hz. There are indications that the kHz QPO frequency decreased from
1160 Hz to 1145 Hz when the count rate increased, which would be quite
different from what is observed in other atoll sources for which kHz QPOs have
been discovered. In the X-ray color-color diagram and hardness-intensity
diagram the source traced out the curved branch (the so-called banana branch)
which has been found by previous instruments. The kHz QPO was only detected
when the source was at the lowest count rates during our observations, i.e. on
the lower part of the banana branch. When 4U 1735-44 was at higher count rates,
i.e. on the upper part of the banana branch and at higher inferred mass
accretion rate with respect to that on the lower part of the banana branch, the
QPO was not detected.
  Besides the kHz QPO we discovered a low frequency QPO with a frequency near
67 Hz, together with a complex broad peaked noise component below 30 Hz. This
67 Hz QPO may be related to the magnetospheric beat-frequency QPO, which is
observed on the horizontal branch of Z sources. This idea is supported by the
(peaked) noise found in both 4U 1735-44 and Z sources at frequencies just below
the QPO frequency.
