A new method for classifying mountain morphology, `mountain ordering,' is proposed, and quantitative expressions for various morphological parameters of two ordered mountains in northern Japan were obtained using this method. Mountain order was defined in terms of the closed contour lines on a topographic map. A set of closed, concentric contour lines defines a first-order mountain. Higher-order mountains can be defined as a set of closed contour lines that contain lower-order mountains and that have only one closed contour line for each elevation; they are identified as m 1th-order mountains, where m represents the order of the enclosed, lower-order mountains. The geomorphometry for a mountain ordered according to this definition permits the identification of systematic relationships between various morphological parameters. The relationships between mountain order and these morphological parameters follow a form similar to that of Horton's laws, and permit the calculation of the ratios of number, area and height; these parameters are sufficient to express the magnitude of a mountain's dissection. The sizeΒ±frequency distribution for area and height shows self-similarity for ordered mountains, and determines their fractal dimensions. Furthermore, the relationship between area and height, which has the form of a power function, describes the relief structure of ordered mountains.