This paper proposes a systematic procedure to identify river reaches from a geomorphic point of view. Their identification traditionally relies on a subjective synthesis of multi-dimensional information (e.g., changes of slope, changes of width of valley bottom). We point out that some of the attributes adopted to describe geomorphic characters of a river (in particular sinuosity and confinement) depend on the length of reaches, while these latter are not yet identified; this is a source of ambiguity and introduces, at least conceptually, an unpleasant, implicit, iterative procedure. We introduce a new method which avoids this difficulty. Furthermore, it is simple, objective, and explicitly defined, and as such, it is automatable. The method requires to define and determine a set of intensive attributes, i.e., attributes that are independent of the segment length. The reaches are then identified by the intersection of the segmentations induced by such attributes. We applied the proposed procedure in two case studies, the Magdalena River (Colombia) and the Baker River (Chile), and investigated whether the adoption of the traditional approach for the definition of reaches would lead to a different result. We conclude that there would be no detectable differences. As such, the method can be considered an improvement in geomorphic river characterization.