  We propose a new Lagrangian describing N=4 superconformal field theory in
three dimensions. This theory is believed to describe interacting field theory
on the worldvolume of a M2-brane on an orbifold, and is obtained as a
Z_2-quotient of the theory proposed by Bagger and Lambert. Despite unusual
Chan-Paton structures, we can take Z_2-orbifold by using SU(2)\times SU(2)
bifundamental representations. We also analyze the moduli space of this theory
and found three branches. With an assumption of a broken U(1) symmetry, the
moduli space is consistent with that of the D2-brane in the strong coupling
limit of Type IIA string theory if the gauge group is O(4). Our action has
manifest Z_2-symmetry exchanging two R^4/Z_2's in M-theory, and this suggests a
new non-perturbative duality between a O2^{-}-brane on orbifold R^4/Z_2 and a
O2^{-}-brane with D6-branes.
