Recently, stochastic computing based on stochastic numbers attracts attention as an effective computation method, which realizes arithmetic operations by simple logic circuits with a tolerance of bit errors. When we input two or more identical values to a stochastic circuit, we require to duplicate a stochastic number. However, if bit streams of duplicated stochastic numbers are dependent on each other, their arithmetic operation results can be inaccurate. In this paper, we propose two stochastic number duplicators, called FSR and RRR. The stochastic numbers duplicated by the FSR and RRR duplicators have the equivalent values but have independent bit streams, effectively utilizing bit re-arrangement using randomized bit streams. Experimental evaluation results demonstrate that the RRR duplicator, in particular, obtains more accurate results even if a circuit has re-convergence paths, reducing the mean square errors by 20%-89% compared to a conventional stochastic number duplicator.