The advent of different approximate accelerated stochastic simulation methods has helped considerably in reducing the computational load of the exact simulation algorithms. However, along with the reduction in the computational load comes the risk of driving the molecular numbers to the regime of negative numbers during the simulations. Over the years, various methods have been developed in order to solve the problem by using different strategies. Some methods have employed binomial numbers to model the reactions, while others have tried the partitioning of the reaction network. In this manuscript, we have proposed a new approach where the noise inherent in the choice of the number of firings of a given reaction during a time step is taken into account. This idea of noise accounting is used in conjunction with the accelerated stochastic method: the Representative Reaction Approach (RRA). It is found that the new method is successful at solving the problem of negative numbers, and compares very favorably with other state-of-the-art stochastic simulation methods.