We have investigated the effects of a high-field region on low-frequency noise (LFN) in AlGaAs/InGaAs HEMTs using a two-region model and experiments. The negative cross-correlation between the LFN generated from a low-field region and that from a high-field region is found for the first time. This negative cross-correlation depends on gate and drain voltages, and increases with gate voltage. Due to this negative cross-correlation, the observed LFN is almost constant because the crosscorrelation cancels out the increase in the LFN generated from the low-field region.