In this note, a novel, Lyapunov-based, variable-gain super-twisting algorithm (STA) is proposed. It ensures for linear time invariant systems the global, finite-time convergence to the desired sliding surface, when the matched perturbations/uncertainties are Lipschitz-continuous functions of time, that are bounded, together with their derivatives, by known functions. The proposed algorithm has similar properties to the variable-gain first-order sliding mode control, but it provides alleviation to the chattering phenomenon. The results are verified experimentally.