For a system of equations \(dx/dt=f(x)\), \(f(0)=0\) where \(x\in R^ n\), \(f:N\to R^ n\), \(N\subset R^ n\) the author introduces the Lyapunov matrix-function (1) \({\mathcal B}(x)=\{w_{ij}(x)\}^ m_{i,j=1}\), \(w_{ij}(0)=0\); \(\bar {\mathcal B}(x)=\max_{i,j}w_{ij}(x)\), i,\(j\in [1,m]\) and its derivative \(\quad (2)\quad\overset \circ {\mathcal B}(x)=\lim_{t\to 0+}\inf (1/t)({\mathcal B}(x(t,x)-\bar {\mathcal B}(x)U),\) where U is an \(m\times m\) matrix with elements \(u_{ij}=1\). By means of function (1) and its derivative (2) La Salle's principle of invariance is determined here.