Let R be a prime ring with involution and char R≠2 . Let f(X1,…Xn)be the noncentral multilinear polynomial over the extended centroid of R and d and δ bethe derivation of R .The surn of the coefficients in f(X1,…, Xn) (denoted by fsc) isnonzero. If d(fsc) =δ(fsc) and d(f(X1,…, Xn)) f(X1,…, Xn ) - f(X,1…,Xn ).δ(f(X1,…,Xn)) is central valued on the traces of R. Then either d =δ= 0 or Rsatisfy S4. Also we give the results when dm (f(X1,…, Xn)) is central valued on thetraces of R. Finally we give some results in semiprime rings.