Remark About Scaling Limit of ABJ Theory

We generalize the suggestion presented in arXiv:0806.3498 that the 3d N=8 superconformal SU(N) Chern-Simons-matter theory of Lorentzian Bagger-Lambert-Gustavson type (L-BLG) can be obtained through the scaling limit from N=6 superconformal U(N)xU(N) Chern-Simons-matter theory of Aharony, Bergman, Jafferis and Maldacena (ABJM) to the case when we study the scaling limit of N=6 superconformal U(M)xU(N) Chern-Simons-matter theory of Aharony, Bergman and Jafferis (ABJ). We show that if we extend the ABJ theory in the same way as in arXiv:0811.1540 we can define a consistent limit that leads to SU(N) L-BLG theory together with U(M-N) Chern-Simons theory of level k.