The impossibility to use the MCMC (Markov chain Monte Carlo) methods for long noisy chaotic time series (TS) (due to high computational complexity) is a serious limitation for reconstruction of dynamical systems (DSs). In particular, it does not allow one to use the universal Bayesian approach for reconstruction of a DS in the most interesting case of the unknown evolution operator of the system. We propose a technique that makes it possible to use the MCMC methods for Bayesian reconstruction of a DS from noisy chaotic TS of arbitrary long duration.