We show that if a 4-spacetime V-4 can be embedded into E(5) then, if b
(ij) is the second fundamental form tensor associated with V-4, the qu
antity (trace b). b(ij)(-1) depends only on intrinsic geometric proper
ties of the spacetime. Such fact is used to obtain,a necessary conditi
on for the embedding of a V-4 into E(5).