  A rotational band with five $\gamma$-ray transitions ranging from 2$^{+}$ to
12$^{+}$ states was identified in $^{40}$Ar. This band is linked through
$\gamma$ transitions from the excited 2$^{+}$, 4$^{+}$ and 6$^{+}$ levels to
the low-lying states; this determines the excitation energy and the spin-parity
of the band. The deduced transition quadrupole moment of 1.45$^{+0.49}_{-0.31}
eb$ indicates that the band has a superdeformed shape. The nature of the band
is revealed by cranked Hartree--Fock--Bogoliubov calculations and a
multiparticle--multihole configuration is assigned to the band.
