We have developed a new scheme with high accuracy and parsimonious memory requirements to reconstruct the source wavefield in reverse time migration (RTM). This scheme used a linear combination of the boundary wavefield in several layers to reconstruct the wavefield in the imaging domain. The value of the linear combination was stored in one buffer, making the computer memory requirement of our method equal to that of a method that only stored one layer of the boundary wavefield. The coefficients for the linear combination were determined by an optimization technique that minimized the finite difference error in the Fourier domain. The optimal coefficients were presented for finite-difference (FD) stencils of 5–15 grid points. The numerical error of our scheme was analyzed and compared with that of standard FD stencils, representing the conventional method that used multiple layers of boundary wavefield to back propagate the source wavefield. The accuracy of our method is only less accurate than the conventional method in theoretical analysis. However, the storage requirement of our method is merely 1/N of the conventional method if a 2N+1 grid-point FD stencil is used in the space. We have also extended the comparison to two other methods, a one-layer method and an extrapolation method, beyond the conventional method. The numerical results demonstrated that our method can accurately generate high-accuracy images in RTM.