The paper presents a new criterion for exponential stability of linear neutral type time delay systems. It is based on the idea to supplement one of the classical conditions of the Krasovskii theorem, namely the positive definiteness of the functional, by a special set of functions satisfying a Razumikhin-type inequality and a similar inequality on the derivative. A functional, whose derivative is given as a negative definite quadratic form, is used. It is shown that this functional admits a quadratic lower bound on the mentioned set of functions.