Due to the continuous demand of small-sized cir- cuits in the fields of image processing and artificial intelligence, stochastic computing has attracted much attention. In stochastic computing, stochastic numbers composed of randomly generated bit streams are used for computation. When inputting two or more identical values to a stochastic circuit, their arithmetic operation results can be inaccurate. In this paper, a stochastic number duplicator called RRR (Register based Re-arrangement circuit using a Random bit stream) duplicator is introduced and is evaluated by applying to composite arithmetic circuits including re-convergence paths. The stochastic numbers duplicated by RRR duplicator have the equivalent values to its input stochastic numbers but have independent bit streams, effectively utilizing bit re-arrangement based on randomized bit streams. It is applied to composite arithmetic circuits and its accuracy and area/delay requirements are evaluated. The results demonstrate that RRR duplicator obtains more accurate results in a circuit with re- convergence paths, reducing the mean square errors by 64%- 94% compared to a conventional stochastic number duplicator.