On the basis of her ethnographic fields in Morocco and Syria, the author discovers a new category in the local classification of kinship: the category of rahim, up till now almost ignored by the specialists. This category is analysed in its behavioural and representational aspects. Its codification in the islamic doctrine is treated as well. With regard to the actual debate about the relevance of cognatic and uterine aspects in arab kinship, it is argued here that the segmentary patrilineal descent model is not simply an ideology, a local representation, or an invention of the structural functionalism. On the contrary, the systems analysed here seem to be based on two opposed and hierarchised principles (like the underlying categories of sex on which they are based) : a structural patrilineal descent principle of group recruitement founded on agnatic solidarity (asabiyya), and a complementary and subordinated cognatic principle defined by the rahim kinship. The rahim kinship identifies an elementary, residual and englobing level of identity and kinship on which dyadic relations between individuals are based.