Reverse time migration (RTM) as a full wave equation method can image steeply dipping structures incorporating all waves without dip limitation. It causes a set of low-frequency artifacts that start to appear for reflection angles larger than 60°. These artifacts are known as the major concern in RTM method. We are first to attempt to formulate a scheme called the leapfrog-rapid expansion method to extrapolate the wavefields and their first derivatives. We have evaluated a new imaging condition, based on the Poynting vectors, to suppress the RTM artifacts. The Poynting vectors information is used to separate the wavefields to their downgoing and upgoing components that form the first part of our imaging condition. The Poynting vector information is also used to calculate the reflection angles as a basis for our weighting function as the second part of the aforementioned imaging condition. Actually, the weighting function is applied to have the most likely desired information and to suppress the artifacts for the angle range of 61°–90°. This is achieved by dividing the angle range to a triplet domain from 61° to 70°, 71° to 80°, and 81° to 90°, where each part has the weight of , , and , respectively. It is interesting to note that, besides suppressing the artifacts, the weighting function also has the capability to preserve crosscorrelation from the real reflecting points in the angle range of 61°–90°. Finally, we tested the new RTM procedure by the BP synthetic model and a real data set for the North Sea. The obtained results indicate the efficiency of the procedure to suppress the RTM artifacts in producing high-quality, highly illuminated depth-migrated image including all steeply dipping geologic structures.