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We examine a natural supersymmetric extension of the bosonic covariant 3-algebra model for M-theory proposed in . It possesses manifest SO(1,10) symmetry and is constructed based on the Lorentzian Lie 3-algebra associated with the U(N) Lie algebra. There is no ghost related to the Lorentzian signature in this model. It is invariant under 64 supersymmetry transformations although the supersymmetry algebra does not close. From the model, we derive the BFSS matrix theory and the IIB matrixdoi:10.4236/jmp.2012.311226 fatcat:q7ynjc4c4vgixhxwsdajqmycle