  We prove explicitly that the general D=3, N=4 Chern-Simons-matter (CSM)
theory has a complete OSp(4|4) superconformal symmetry, and construct the
corresponding conserved currents. We re-derive the OSp(5|4) superconformal
currents in the general N=5 theory as special cases of the OSp(4|4) currents by
enhancing the supersymmetry from N=4 to N=5. The closure of the full OSp(4|4)
superconformal algebra is verified explicitly.
