Discretization of protein conformational space and fragment assembly methods simplify the search of native structures. These methods, mostly of Monte Carlo and genetic-type, do not exploit, however, the fact that short fragments describing consecutive parts of proteins are conformation-dependent. Yet, this information should be useful in improving ab initio and comparative protein structure modeling. In a preliminary study, we have assessed the possibility of using greedy algorithms for protein structure reconstruction based on the assembly of fragments of four-residue length. Greedy algorithms differ from Monte Carlo and genetic approaches in that they grow a polypeptide chain one fragment after another. Here, we move one step further in complexity, and provide strong evidence that the dependence between consecutive local conformations during assembly makes possible the reconstruction of protein structures from their secondary structures using a Go potential. Overall our procedure can reproduce 20 protein structures of 50-164 amino acids within 2.7 to 6.5 A RMSd and is able to identify native topologies for all proteins, although some targets are stabilized by very long-range interactions.