  We introduce an anti-symmetric metric into a 3-algebra and call it a
symplectic 3-algebra. The N=6, Sp(2N) X U(1) superconformal Chern-Simons-matter
theory with SU(4) R-symmetry in three dimensions is constructed by specifying
the 3-brackets in a symplectic 3-algebra. We also demonstrate that the N=6,
U(M) X U(N) theory can be recast into this symplectic 3-algebraic framework.
