Despite the recent advances in developing more effective thresholding methods to convert weighted networks to unweighted counterparts, there are still several limitations that need to be addressed. One such limitation is the inability of the most existing thresholding methods to take into account the topological properties of the original weighted networks during the binarization process, which could ultimately result in unweighted networks that have drastically different topological properties than the original weighted networks. In this study, we propose a new thresholding method based on the percolation theory to address this limitation. The performance of the proposed method was validated and compared to the existing thresholding methods using simulated and real-world functional connectivity networks in the brain. Comparison of macroscopic and microscopic properties of the resulted unweighted networks to the original weighted networks suggests that the proposed thresholding method can successfully maintain the topological properties of the original weighted networks.