The extremely rapid burst of TeV photons from Mkn 421 ( 15 May 1996 ) can be reconciled with the standard properties of a relativistic \gamma -ray emitting jet ( bulk Lorentz factor \Gamma \sim 10 ; \mbox { size } \sim 10 ^ { 17 } cm ) if one assumes that the electrons are accelerated in conical shocks with both opening and viewing angles \approx 1 / \Gamma . If the injection time and the cooling time are much less than the photon crossing time , an emission ring moves along the jet and leads to the appearance of a very rapid flare , in satisfactory agreement with the observations .