A tetraxial fabric and a weaving machine for manufacturing the fabric. The tetraxial fabric is formed by the crisscross of warp yarns, weft yarns, and bias yarns having two different diagonal directions. A first set of warp yarns is overlaid by the weft yarns and, in turn, overlies the bias yarns. A second set of warp yarns, which alternate with the warp yarns in the first set, overlies the weft yarns and is, in turn, overlaid by the bias yarns. Due to the yarn formation, the fabric has a constant isotropy and evenness and can be made with a fill coefficient of up to 100%. The weaving machine for the manufacture of the tetraxial fabric can alternately produce, in the fabric formation area, two sheds between the warp yarns for passing the weft yarns at opposite sides with respect to the bias yarns.