A warp knitting machine using warp and weft threads produces a fabric with a woven appearance on one side. The machine has at least one forward thread system for forming stitches and at least one rearward thread system for forming stitches. This rearward thread system is successively operable to reciprocally form a common stitch with a corresponding pair of the warp threads of the forward thread system. A weft thread magazine can repetitively place weft threads between the forward and rearward thread system. The forward thread system is successively operable to reciprocally lay a portion of each of its warp threads at one of two corresponding, alternate wales over at least one of the weft threads. The rearward thread system is operable to lay its warp threads behind the weft threads. Before making a stitch, the forward thread system performs at least one overlap of at least two needle spaces while the rearward thread system is displaced to reciprocally lay its warp thread about needles onto which adjacent warp threads of the forward thread system are laid.