  The van der Waals ferromagnet (FM), VI$_3$, was studied by muon spin
relaxation ($\mu^+$SR) and first principle calculations based on density
functional theory (DFT). Temperature dependent zero field muon spin relaxation
($\mu^+$SR) measurements confirm the onset of long range FM order and the time
spectra exhibits clear muon spin precession frequencies for $T<T_{\rm
C}=50.03(1)$~K. The calculated internal magnetic fields at the predicted muon
sites, based on the established magnetic structure from neutron diffraction, is
inconsistent with the measured one. This inconsistency is because of strong
incoherent neutron scattering and absorption originating from the elements V
and I. Instead, a new and a more accurate magnetic structure is derived based
on a combined study using $\mu^+$SR and DFT. These results suggest strong
contritions from orbital angular momentum, providing experimental evidence for
the existence of unquenched orbital angular momentum of V$^{3+}$ in VI$_3$.
Finally, an unusual form of a short range ordering is present above $T_{\rm
C}$. Its temperature dependence is unlike previously reported cases in other
layered compounds and its microscopic origin is discussed.
