We have identified for the first time an energy‐time dispersion of precipitating electron flux in a pulsating aurora patch, ranging from 6.7 to 580 keV, through simultaneous in‐situ observations of sub‐relativistic electrons of microburst precipitations and lower‐energy electrons using the Loss through Auroral Microburst Pulsation sounding rocket launched from the Poker Flat Research Range in Alaska. Our observations reveal that precipitating electrons with energies of 180–320 keV were observed first, followed by 250–580 keV electrons 0–30 ms later, and finally, after 500–1,000 ms, 6.7–14.6 keV electrons were observed. The identified energy‐time dispersion is consistent with the theoretical estimation that the relativistic electron microbursts are a high‐energy tail of pulsating aurora electrons, which are caused by chorus waves propagating along the field line.