  Very thin free-flowing liquid sheets are promising targets for
high-repetition-rate laser-ion acceleration. In this work, we report the
generation of micrometer-thin free-flowing liquid sheets from the collision of
two liquid jets, and study the vibration and jitter in their surface normal
direction. The dependence of their motion amplitudes on the generation
parameters is studied in detail. The origins of the vibration and jitter are
discussed. Our results indicate that when the generation parameters are
optimized, the motion amplitudes in the stable region can be stabilized below
3.7 {\mu}m to meet the stringent requirement of sheet position stability for a
tight-focusing setup in laser-ion acceleration experiments.
