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The problem of stability for linear time-delay systems of neutral type is taken into consideration. A new extensively augmented Lyapunov-Krasovskii functional is introduced and a sufficient delay-dependent stability criterion is derived in terms of linear matrix inequalities (LMIs). Utilisation of any model transformation method or any kind of bounding for the cross terms are avoided in the stability analysis. Moreover, in order to reduce the complexity of the solution of the LMI set, the proposed method does not also employ any free weighting matrix relaxation approach. Two numerical examples are illustrated to indicate the effectiveness of the proposed method.