  Superdeformed (SD) states in $^{40}$Ar have been studied using the
deformed-basis antisymmetrized molecular dynamics. Low energy states were
calculated by the parity and angular momentum projection (AMP) and the
generator coordinate method (GCM). Basis wave functions were obtained by the
energy variation with a constraint on the quadrupole deformation parameter
$\beta$, while other quantities such as triaxiality $\gamma$ were optimized by
the energy variation. By the GCM calculation, an SD band was obtained just
above the ground state (GS) band. The SD band involves a $K^\pi = 2^+$ side
band due to the triaxiality. The calculated electric quadrupole transition
strengths of the SD band reproduce the experimental values appropriately.
Triaxiality is significant for understanding low-lying states.
