In an early work by Dunlap et al. (1990) it was conjectured, using a matrix-transfer approach, that diagonal-disordered systems with local correlation (dimer-models) exhibit an absence of Anderson localization. In this letter we find explicitly these delocalized states, and energies, using a suitable unitary transformation and the symmetries related to the model. Moreover, we expand these states around the critical energy and find a new 1/ square root (E-Ec) divergence.