The behavior of self focusing of the ultra short intense laser pulse during propagating in atmosphere was studied, particularly, using the numeric solution of a time dependent Schdinger equation on account of Kerr effect and multi photon ionization (MPI) effect. The result implies the intermittence, rather than the stable structure, of the filamentation caused by self focusing. Each on axis filamentation will decay due to the ionization while the off axis energy will replenish to the on axis region intermittently due to Kerr effect.