A reinforcing textile complex for composite materials, comprising a stack of textile layers with a view to their impregnation by a polymer resin, the including complex comprising: • an assembly of weft threads (2); • an assembly of warp threads (3, 4) associated in pairs, each pair comprising two threads of different type, at least one of which (3) is based on high toughness threads, the two threads of a given pair being woven with the weft threads in a "leno" weave.