We propose an interpolation algorithm for one-way wave equation migration, which can allow the migration to take much bigger extrapolation step than usual, and is still accurate up to the dip limit of the one way propagator. The proposed interpolation algorithm is frequency dependent and applicable to any one way extrapolator which works in the frequency domain. It requires that there be limited vertical variation in the velocity model within each extrapolation step. Numerical tests have validated our algorithm and showed significantly speed up of the migration with barely noticeable deterioration of the image quality.