Knowledge of past plate motions derived from ocean-floor finite rotations is an important asset of the Earth Sciences, because it allows linking a variety of shallow-rooted and deep-rooted geological processes. Efforts have recently been taken toward inferring finite rotations at the unprecedented temporal resolution of 1 Myr or less, and more data are anticipated in the near future. These reconstructions, like any data set, feature a degree of noise that compromises significantly our ability to make geodynamical inferences. Bayesian Inference has been recently shown to be effective in reducing the impact of noise on plate kinematics inferred from high-temporal-resolution finite-rotation data sets. We describe REDBACK, an open-source software that implements transdimensional hierarchical Bayesian Inference for efficient noise-reduction in plate kinematic reconstructions. Algorithm details are described and illustrated by means of a synthetic test.