In this paper, the global optimization problem with a multiextremal objective function satisfying the Lipschitz condition over a hypercube is considered. An algorithm that belongs to the class of information methods introduced by R.G. Strongin is proposed. The knowledge of the Lipschitz constant is not supposed. The local tuning on the behavior of the objective function and a new technique, named the local improvement, are used in order to accelerate the search. Two methods are presented: the first one deals with the one- dimensional problems and the second with the multidimensional ones (by using Peano-type space-filling curves for reduction of the dimension of the problem). Convergence conditions for both algorithms are given. Numerical experiments executed on more than 600 functions show quite a promising performance of the new techniques.