The domain structure in in-plane magnetized Fe/Ni/W(110) films is investigated using spin-polarized low-energy electron microscopy. A novel transition of the domain wall shape from a zigzag-like pattern to straight is observed as a function of the film thickness, which is triggered by the transition of the domain wall type from out-of-plane chiral wall to in-plane Neel wall. The contribution of the Dzyaloshinskii-Moriya interaction to the wall energy is proposed to explain the transition of the domain wall shape, which is supported by Monte-Carlo simulations.