The fast disruption of the runaway electrons-beam in a high-voltage picosecond atmospheric-discharge [G. A. Mesyats and M. I. Yalandin, IEEE Trans. Plas. Sci. 37 785 ( 2009)] is considered. The plasma electrostatic instabilities are proposed as a mechanism of such disruption. Strong over-voltage (more than 1 MV/cm at gas pressure 1 atm) provides an intense electrons-acceleration in the runaway regime. It is shown that neither collisions nor a static potential profile could deliberately prevent this runaway regime. Whereas, the cathodeanode bridging impossible within tens of pisoseconds. It is obtained that the characteristic times of a simplest electrostatic-instabilities build-up are consistent with the observed runaway-electrons beam-duration at the certain plasma density, which was considered as a parameter. The agreement our estimation results and the measurements [G. A.