In this paper, we present a new manner for computing the so called new form of the functional of complete type for neutral type time-delay systems without assumptions of continuity and differentiability on the initial function. It is obtained by using a new Cauchy formula. We present briefly the necessary stability conditions depending on the delay Lyapunov matrix that this result makes possible to prove. (C) 2016, IFAC (International Federation of Automatic Control) Hosting by Elsevier Ltd. All right reserved.