The construction of Lyapunov-Krasovskii functionals for linear time-delay system depends on so-called Lya-punov matrix. We study the problem of finding this matrix by solving the delay-free equations with specific boundary conditions. The special boundary conditions for the delay-free problem are found and it is shown, that the problem of Lyapunov matrix' finding as a solution of the boundary value problem with delay and the delay-free problem are equivalent.