This short note presents a constructive way of reducing monotone LCPs (linear complementarity problems) over cones to LPs (linear programs) over cones. In particular, the monotone semidefinite linear complementarity problem (SDLCP) in symmetric matrices, which was recently proposed by Kojima, Shindoh and Hara, is reducible to an SDP (semidefinite program). This gives a negative answer to their question whether the monotone SDLCP in symmetric matrices is an essential generalization of the SDP.