Molecular motors have inspired many avenues of research for nanotechnology but most molecular motors studied so far allow only unidirectional movement. The archaeal RNA-exosome is a reversible motor that can either polymerize or degrade an RNA strand, depending on the chemical environments. We developed a single molecule fluorescence assay to analyze the real time locomotion of this nanomachine on RNA. Despite the multimeric structure, the enzyme followed the Michaelis-Menten kinetics with the maximum speed of ∼3 nucleotides/s, showing that the three catalytic cylinders do not fire cooperatively. We also demonstrate rapid directional switching on demand by fluidic control. When the two reaction speeds are balanced on average, the enzyme shows a memory of the previous reaction it catalyzed and stochastically switches between primarily polymerizing and primarily degrading behaviors. The processive, reversible, and controllable locomotion propelled by this nanomachine has a promising potential in environmental sensing, diagnostic, and cargo delivery applications.