In our recent series of papers, we have used the structures of statistical significance from Monte Carlo simulations to improve the predictions of secondary structure of RNA and to analyze the possible role of locally significant structures in the life cycle of human immunodeficiency virus. Because of intensive computational requirements for Monte Carlo simulation, it becomes impractical even using a supercomputer to assess the significance of a structure with a window size greater than 200 along an RNA sequence of 1000 bases or more. In this paper, we have developed a new procedure that drastically reduces the time needed to assess the significance of structures. In fact, the efficiency of this new method allows us to assess structures on the VAX as well as the CRAY.