The invention relates to a process for assembling materials by means of a riveting member of the type comprising a mandrel (2) and a sleeve (1). The sleeve (1) is provided with a peripheral recess on its external surface, in particular a groove (5), for forming a bending zone, while the mandrel has a head (9) able to deform the tubular end of the sleeve and to fold it back at the level of its bending zone. During riveting, the peripheral recess of the sleeve preserves the starting point of the countersink of the material against any stress and the bending zone of the sleeve permits providing a bearing surface of great dimension applied precisely against the materials.