Primary reflections, like multiples, can generate false images when reverse time migration (RTM) algorithms are used. The false images are formed by the zero-lag correlation of the source wavefields and primary reflections, which are propagated by the migration algorithm along nonphysical paths. These paths are generated by strong velocity gradients or reflection interfaces when the two-way wave equation is used. Conceptually, this type of artifact can be removed by separating up- and downgoing waves, but such separation may be impractical because it often requires storing the entire wavefields at all time steps. We have developed a de-primary RTM method in which such separation can be accomplished without saving the wavefields. The computational cost of the proposed method was only approximately 33% higher than that of conventional RTM algorithms. Using field and synthetic data sets, we have demonstrated the existence of this endemic RTM problem and verified the effectiveness of the de-primary RTM technique for removing the false events.