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Apart from their central role during 3D structure determination of proteins the backbone chemical shift assignment is the basis for a number of applications, like chemical shift perturbation mapping and studies on the dynamics of proteins. This assignment is not a trivial task even if a 3D protein structure is known and needs almost as much effort as the assignment for structure prediction if performed manually. We present here a new algorithm based solely on 4D [H-1, N-15]-HSQC-NOESY-[H-1, N-15]-HSQC spectra which is able to assign a large percentage of chemical shifts (73-82 %) unambiguously, demonstrated with proteins up to a size of 250 residues. For the remaining residues, a small number of possible assignments is filtered out. This is done by comparing distances in the 3D structure to restraints obtained from the peak volumes in the 4D spectrum. Using dead-end elimination, assignments are removed in which at least one of the restraints is violated. Including additional information from chemical shift predictions, a complete unambiguous assignment was obtained for Ubiquitin and 95 % of the residues were correctly assigned in the 251 residue-long N-terminal domain of enzyme I. The program including source code is available at https://github.com/thomasexner/4Dassign.