The range-Doppler algorithm is quite popular in airborne synthetic aperture radar (SAR) image formation. To reduce the excessive computation load associated with the pixel by pixel interpolation required in traditional range Doppler algorithm (RDA) to remove range cell migration (RCM), a fast and interpolation-free range cell migration correction(RCMC) technique which only involves operations of two FFTs and one complex multiplication was proposed. Based on the analysis of echo signal model, the constraint on attainable maximum swath with such a fast RCMC technique was derived, and the relation between this constraint and the imaging resolution was also given. The analysis was validated by simulation results. The theoretical analysis, simulation and SAR real data processing result show that this technique can reduce the computational burden dramatically with high enough precision, and is amenable to on-board real time processing.