Let R be a 2-torsion free semiprime ring. Suppose that there exists a 4-permuting 4-derivation ${Delta}:R{ imes}R{ imes}R{ imes}R{ ightarrow}R$ such that the trace is centralizing on R. Then the trace of ${Delta}$ is commuting on R. In particular, if R is a 3!-torsion free prime ring and ${Delta}$ is nonzero under the same condition, then R is commutative.