Quadratic Lyapunov functionals with a given time derivative for the case of neutral type time delay systems have been presented in Rodriguez et al. ("Robust stability of neutral systems: a Lyapunov-Krasovskii constructive approach", International Journal of Robust and Nonlinear Control, 14, pp. 1345-1358, 2004). In this contribution a new form of the functionals is proposed. The functionals now do not include the time derivative of the system state. This modification provides new quadratic bounds for the functionals and makes them useful in computation of exponential estimates for solutions of the systems, as well as in calculation of the robustness bounds. Special attention has also been paid to the Lyapunov matrices which define the functionals. A new definition of the matrices is given, and their properties are analysed in detail.