In this article the new integral conditions \(\sup_{| \lambda | >1}(| \lambda |^ 2-1)\int^{2\pi}_{0}\| (T-\lambda)^{- 1}u\|^ 2d\theta \leq C\| u\|^ 2\) and \(\sup_{| \lambda | >1}(1-| \lambda |^{-2})\int^{2\pi}_{0}\| (T^*- \lambda)^{-1}u\|^ 2d\theta \leq C\| u\|^ 2\) (u\(\in H)\) on the resolvent of the operator T are given, necessary and sufficient for the operator T to be similar in the Hilbert space H to a unitary operator.