The one dimensional dimer model is investigated and the localization length calculated exactly. The presence of delocalized states at Ec = ǫ a,b of two possible values of the chemical potential in case of | ǫa − ǫ b |≤ 2 is confirmed and the corresponding indices of the localization length were calculated. The singular integral equation connecting the density of states with the inverse of the localization length is solved and the analytic expression for the density of states compared with the numerical calculations.After Anderson's works [1], [2] it became clear that all states of the systems in one or two dimensional spaces, which are putted into the fully disordered potential field (independent site-energy disordered Anderson model), are exponentially localized. In [3]-[6] it has been shown, that this claim is true for any strength of disorder and the localization is present in less than three dimensions even for an infinitesimal amount of full disorder. The idea arises that the type of disorder underlies of localizationdelocalization (insulator-metal) transition of one dimensional systems and in order to understand its nature we need to investigate the conditions, under which delocalized states can appear. That is why it is necessary to consider experimentally [25] and theoretically [7]-[24] one-dimensional systems with short(or long)-range correlated disorder, where the random variables are not fully independent, but are correlated at short (long) distances. The vanishing of the localization and the appearance of diffusion of electrons by correlations was further put forward for the explanation of high conductivity of polymers such as doped polyaniline, which can be approached by random-dimer model [8], [11]. The transport properties of random semiconductor superlattices also exhibit [23,24,25] delocalization in case of correlated disorder.One of the simplest tight-binding and numerically best studied model with the nearest-neighbor correlated disorder is the random-dimer model [9]-[14], where one (or both) of the two possible values of site potentials ǫ a and ǫ b are random in pairs and appearing with probabilities p and 1−p. In these papers authors have analyzed the mentioned model and it was shown numerically that initially localized electron can become delocalized if |ǫ a − ǫ b | ≤ 2t (here t is a constant electron hopping coefficient). In the paper [15] the authors have studied the dimer model by numerical and semi-analytical methods. In case when both site potentials appear in pairs, they have calculated the critical energies coinciding with results of [9], and correlation length index ν = 2 (superdiffusion) when |ǫ a − ǫ b | < 2t, and equal to 1 for |ǫ a − ǫ b | = 2t. They present also some calculations of the density of states and the correlation length indices for different values p for the probability. In the papers [16], [17] similar results were obtained by use of numerical methods. An interesting analytic approach was developed in [18].Since in all papers above the calculations were done mainly n...