Staggered synthetic aperture radar (SAR) is an innovative concept, where the pulse repetition interval (PRI) is continuously varied. This, in combination with digital beamforming (DBF) on receive, allows high-resolution imaging of a wide continuous swath without the need for a long antenna with multiple apertures. However, staggered-SAR systems require a mean pulse repetition frequency (PRF) much larger than the signal Doppler bandwidth and allow the use of transmitted pulses of limited length. This letter proposes a novel processing strategy for staggered SAR data, which allows a reduction of the mean PRF and the use of longer transmitted pulses. The performance obtained with the proposed novel strategy is evaluated and compared with a conventional SAR system operating with constant PRI.