Suppose \(A\) is a \(C^*\)-algebra and let \(M(A)\) be its multiplier algebra. A linear mapping \(T\) defined on a dense subspace of \(A\) is said to be affiliated with \(A\), if there exists a multiplier \(z\in M(A)\), \(\| z\|\leq 1\) such that \(T[(1- z^* z)^{{1\over 2}} a]= za\), \(\forall a\in A\). Theorem. If \(U_ t (t\in \mathbb{R})\) is a strictly continuous unitary group in \(M(A)\), there exists a self-adjoint element \(h\) affiliated with \(A\) such that \(U_ t= \exp(ith)\). When \(U_ t\) is norm continuous, then \(h\in M(A)\).