Normal moveout (NMO) correction is routinely applied to traces of each common-midpoint (CMP) gather before forming a stack section. Conventional NMO correction has the drawback of producing stretching as a natural result of convergence of the NMO trajectories. Although this problem exists on completely hyperbolic reflections, the reflections will be further deviated from the desirable zero-offset equivalent if they indicate nonhyperbolic behavior. We have addressed this issue and developed a new method of stretch-free NMO correction in two steps: first, a novel way of rectifying NMO correction trajectories in a shifted hyperbolic NMO base, and second, a prioritized successive process of mapping data samples into an NMO-corrected gather. We have determined the advantage of the proposed method over two preceding methods: isomoveout and local stretch zeroing. The effectiveness of the new method in producing a stretch-free NMO gather was tested on synthetic data generated by ray tracing and a real data set of 200 CMP gathers of an Iranian oil field. The proposed method can be used in the presence of hyperbolic and nonhyperbolic events, and it recovers the amplitudes of interfering reflections to extend the usable offsets.