Two categories of reference constitute the socialorganisation of Albanese society. The notion of fisi(‘lineage’) represents the first, which is typifying,segmentary and holistic, while the second,classifying, linear and individualising is representedin the notion of lisi i gjakut (‘tree of blood’). Thesecategories do not oppose each other as both pertainto a common logic of patrilineal filiation. Unlike the segmentary regime, the linear one does notallow to account for the previous generations.Thus, when a large number of collateral parentsacknowledge themselves as being part of a common‘tree of blood’, they still have to qualify thisthrough a second symbolic and hereditary markerwhich, from a vertical axis, will complete the lackof memory and/or of ramification. A fixation ofthe patronymic name in the broad sense - thetransmissible family name - becomes thennecessary. This ordered complementarity betweenthe segmentary and the linear reveals itself as asociological operator the hierarchical nature ofwhich allows the transactional opening in strategicrelations oriented towards the other.