Metamagnetism occuring inside a ferromagnetic phase is peculiar. Therefore, Sr4Ru3O10, a T C = 105 K ferromagnet, has attracted much attention in recent years, because it develops a pronounced metamagnetic anomaly below T C for magnetic fields applied in the crystallographic ab-plane. The metamagnetic transition moves to higher fields for lower temperatures and splits into a double anomaly at critical fields H c1 = 2.3 T and H c2 = 2.8 T, respectively. Here, we report a detailed study of the different components of the magnetization vector as a function of temperature, applied magnetic field, and varying angle in Sr4Ru3O10. We discover for the first time a reduction of the magnetic moment in the plane of rotation at the metamagnetic transition. The anomaly shifts to higher fields by rotating the field from H ⊥ c to H || c. We compare our experimental findings with numerical simulations based on spin reorientation models taking into account magnetocrystalline anisotropy, Zeeman effect and antisymmetric exchange interactions. While Magnetocrystalline anisotropy combined with a Zeeman term are sufficient to explain a metamagnetic transition in Sr4Ru3O10, a Dzyaloshinskii-Moriya term is crucial to account for the reduction of the magnetic moment as observed in the experiments.