We have identified for the first time an energy-time dispersion of precipitating electron flux in a pulsating aurora patch, ranging from 6.7 keV to 580 keV, through simultaneous in-situ observations of sub-relativistic electrons of microburst precipitations and lower-energy electrons using the LAMP 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 500-1000 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.