Let .R; / be a 2-torsion free-prime ring with involution and center Z.R/, U a nonzero square closed-Lie ideal of R. An additive mapping F W R ! R is called a generalized derivation if there exits a derivation d W R ! R such that F .xy/ D F .x/y Cxd.y/. In the present paper, we prove that U Â Z.R/ if any one of following conditions holds: 1) OEF .u/; u D 0; 2) OEd.u/; F .v/ D 0; 3) d.u/oF .v/ D 0; 4) OEd.u/; F .v/ D˙OEu; v; 5) d.u/oF .v/ D˙uov; 6) d.u/F .v/˙uv 2 Z.R/; for all u; v 2 U: Furthermore, an example is given to demonstrate that the-primeness hypothesis is not superfluous.