The properties of rivers and their catchments can be expressed by statistical relationships between geomorphic parameters. These statistical relationships may reveal some inherent differences in geomorphic evolution for different reaches or different order tributaries of a river basin. A case study was undertaken of the Yunnan reach of the Langcangjiang River. The catchment area, channel length and gradient of the first-, second- and third-order tributaries all with catchment areas larger than 100 km2 in the Yunnan reach were the main geomorphic parameters evaluated. The correlation between catchment area and channel length as well as between catchment area and channel gradient with respect to the total tributaries, different reach tributaries, and different order tributaries were revealed using statistical methods. In general, the channel length as a function of catchment area, was best expressed by a quadratic function where channel length increases with increasing catchment area (half parabola), while the channel gradient as a function of catchment area is best expressed by an exponential decay function. Comparison of the best-fit formulas revealed the following phenomena: the lower Yunnan reach tributaries and the first-order tributaries have a dominant effect on geomorphic parameters of the total tributaries. In addition, the statistical relationships indicate that the river geomorphic system in the upper and lower Yunnan reaches evolved differently. This study method used to differentiate river characteristics by determining statistical relationships between geomorphic parameters may be extended to other rivers and their catchments.