We found that a three-step high-temperature annealing leads to intrinsic gettering in oxygen-lean Czochralski silicon grown in a magnetic field as well as in oxygen-free float zone silicon. Such thermal treatment has been used thus far for achieving intrinsic gettering only in oxygen-rich Czochralski silicon. We present experimental characteristics of this new intrinsic gettering process, and we propose a phenomenological explanation involving outdiffusion and precipitation of silicon interstitials rather than oxygen which is involved in the standard intrinsic gettering.