  The contribution of the magnetic field to the formation of high-mass stars is
poorly understood. We report the high-angular resolution
($\sim0.3^{\prime\prime}$, 870 au) map of the magnetic field projected on the
plane of the sky (B$_\mathrm{POS}$) towards the high-mass star forming region
G333.46$-$0.16 (G333), obtained with the Atacama Large Millimeter/submillimeter
Array (ALMA) at 1.2 mm as part of the Magnetic Fields in Massive Star-forming
Regions (MagMaR) survey. The B$_\mathrm{POS}$ morphology found in this region
is consistent with a canonical ``hourglass'' which suggest a dynamically
important field. This region is fragmented into two protostars separated by
$\sim1740$ au. Interestingly, by analysing H$^{13}$CO$^{+}$ ($J=3-2$) line
emission, we find no velocity gradient over the extend of the continuum which
is consistent with a strong field. We model the B$_\mathrm{POS}$, obtaining a
marginally supercritical mass-to-flux ratio of 1.43, suggesting an initially
strongly magnetized environment. Based on the Davis-Chandrasekhar-Fermi method,
the magnetic field strength towards G333 is estimated to be 5.7 mG. The absence
of strong rotation and outflows towards the central region of G333 suggests
strong magnetic braking, consistent with a highly magnetized environment. Our
study shows that despite being a strong regulator, the magnetic energy fails to
prevent the process of fragmentation, as revealed by the formation of the two
protostars in the central region.
