In this paper we present another characterization of (${pm}1$)-invariant sequences. We also introduce truncated Fibonacci and Lucas sequences of the second kind and show that a sequence $x;{in};R^{infty}$ is (-1)-invariant(l-invariant resp.) if and only if $D[_x^0]$ is perpendicular to every truncated Fibonacci(truncated Lucas resp.) sequence of the second kind where $$D=diag((-1)^0,; (-1)^1,;(-1)^2,{ldots})$$.