Let A standard operator algebra which does not contain the identity operator, acting on a Hilbert space of dimension greater than one. If ${Phi}$ is a bijective Lie map from A onto an arbitrary algebra, that is $${phi}$$(AB-BA)=$${phi}(A){phi}(B)-{phi}(B){phi}(A)$$ for all A, B${in}$A, then ${phi}$ is additive. Also, if A contains the identity operator, then there exists a bijective Lie map of A which is not additive.