Experimental and theoretical investigations of a diffuse jet (streamer) of apokampic discharge are carried out for various values of air pressure. It is established experimentally that this regime of pulse-periodic discharge is formed stage by stage. At the first stage, in a microsecond discharge of a voltage pulse of positive polarity, a potential spark channel formed during the first pulses between two needle electrodes is transformed into a diffuse channel. At the second stage, a weakly glowing halo is formed near the discharge channel, and a bright offshoot arises near the bending point. Finally, at the third stage of discharge in the steadystate mode, for frequencies of a few to tens of kilohertz in each pulse, the offshoot becomes a source of plasma bullets (streamers) moving with a velocity of up to 200 km/s. As a result of simulation of a streamer in atmospheric pressure air under conditions corresponding to the experimental data, a propagation velocity of up to 400 km/s is obtained for the streamer. It is shown that the formation of a jet significantly depends on the air temperature.