A new approach for multilevel thresholding based on two interesting properties of the histogram is proposed. First, a peak-finding algorithm is presented based on the symmetry of a histogram, for which the hillsides of each hill are symmetrical about the central curve. Next, the duality that the peaks and valleys are opposite is presented in order to identify the valleys of the histogram. Based on this property, we propose a valley-finding algorithm to construct the hierarchical order of the various valleys. The proposed method is computationaily faster than traditional ones such as the variance-based and entropy-based methods. Compared with recent work proposed by Lim, the proposed method has some advantages in constructing the hierarchical order of various valleys.