  We present magnetization measurements on Sr4Ru3O10 as a function of
temperature and magnetic field applied perpendicular to the magnetic easy
$c$-axis inside the ferromagnetic phase. Peculiar metamagnetism evolves in
Sr4Ru3O10 below the ferromagnetic transition $T_{C}$ as a double step in the
magnetization at two critical fields $H_{c1}$ and $H_{c2}$. We map the $H-T$
phase diagram with special focus on the temperature range 50\,K $\le T \le
T_{C}$. We find that the critical field $H_{c1}(T)$ connects the field and
temperature axes of the phase diagram, whereas the $H_{c2}$ boundary starts at
2.8\,T for the lowest temperatures and ends in a critical endpoint at (1\,T;
80\,K). We conclude from the temperature dependence of the ratio
$\frac{Hc1}{Hc2}(T)$ that the double metamagnetic transition is an intrinisc
effect of the material and it is not caused by sample stacking faults such as
twinning or partial in-plane rotation between layers.
