The effect of refractive index fluctuations on the filamentation of a subterawatt femtosecond pulse on kilometer-long path in the turbulent atmosphere is investigated. A novel method of numerical simulation of the pulse filamentation on a long atmospheric path is proposed. The method involves analytical solutions for the chirped pulse, propagating in the air. Detailed pattern of filamentation in the phase-modulated pulse at the distances more than one kilometer is given.