We propose a new Lagrangian describing N = 4 superconformal field theory in three dimensions. This theory is believed to describe interacting field theory oil the worldvolume of a M2-brane oil art 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) x SU(2) bifundanlental representations. We also analyze the moduli space of this theory and found three branches. With all assumption of a broken U(1) symmetry, the moduli space is consistent with that of the D2-hrane 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 O(2-)-brane on orbifold R(4)/Z(2) and a O(2-)-brane with D6-branes. (c) 2008 Elsevier B.V. All rights reserved.