Triaxial textile armature for making high quality composite materials comprising a central layer of axial yarns and at least two side layers of axial yarns. The side layers of axial yarns are placed on opposite sides with regard to the central layer of axial yarns. The axial layers are crosslinked by two directions of bias yarns. The bias yarns of the first direction pass through the central layer of axial yarns in even intervals between axial yarns. The bias yarns of the second direction pass through the central layer of axial yarns in odd intervals between axial yarns. An elementary pattern is formed of twelve axial yarns arranged in three layers, wherein the yarns of the central layer are placed in quincunxes with regard to the axial yarns of the side layers, linked by two crossed sets of N bias yarns each, wherein each bias yarn passes alternatively over six axial yarns and under six axial yarns while crossing 2*N yarns of the other bias direction. The invention also relates to a process for making such armature and a composite material part comprising such armature