Combining through-focus high-resolution transmission electron microscopy and hierarchical multiscale simulations consisting of density-functional theory, analytical empirical potentials, and continuum elastic theory we demonstrate the existence of a new dislocation type in GaN. In contrast with all previously identified or suggested dislocation structures in GaN, all core atoms are fully coordinated; i.e., no broken bonds occur, implying that the dislocation should be electrically inactive. However, as we show, the giant local strain-field around the dislocation core, in combination with the small lattice constant of GaN, causes deep defect states and thus electrically active edge dislocations independent on the specific core structure.