A nonlinear control law is designed for finite-time stabilization of a chain of integrators. The method is based on Implicit Lyapunov Function (ILF) technique and homogeneity properties. The scheme of control parameters selection is presented by a Linear Matrix Inequality (LMI). The method is simple in implementation and does not assume on-line procedure for computation of the ILF value at the current state that is an improvement with respect to [9], [13]. The control law is presented in an explicit form and allows to find the values of all control parameters, that make the solution one of the most constructive. The theoretical results are supported by numerical example.